DETERMINATION OF THE DETONATION WAVE STRUCTURE
Numerical solution of the equations determining the detonation wave structure, assuming steady one-dimensional flow and perfect behavior of reactant and products
ONE-DIMENSIONAL FLOW↗
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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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Wave propagation in a random medium - A complete set of the moment equations with different wavenumbers
The propagation of waves in a random medium is studied in the 'quasi-optics' and the 'Markov random process' approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of moment equations with different transverse coordinates and different wave numbers is then obtained from the Fokker-Planck equation of the characteristic functional. The application of those results to the pulse smearing of the pulsar signal and the frequency correlation function of the wave intensity in interstellar scintillation is briefly discussed.
Lee, L. C.↗
Stratospheric warmings diagnosed using the transformed Eulerian-mean equations and the effect of the mean state on wave propagation
Terms for the transformed Eulerian equations are calculated in order to characterize the phenomenom of sudden stratospheric warming. The transformed diagnostics are applied to data for warmings during Dec. and Jan. 1976-1977, as well as cross sections for the directions of the Eiliassen-Palm (EP) fluxes and residual mean meridional circulations. The convergence of the EP flux was determined to provide a strong approximation to the total effect of waves in forcing the zonal mean flow. The EP fluxes change from an upward and equatorward direction to an upward and poleward direction during the warmings, and indications are reported that the effect is due to a feedback on wave propagation of an evolving mean flow. Ray paths in the meridional plane are computed for different mean wind fields to determine the direction of wave propagation according to linear theory based on the WKB approximation.
Oneill, A.↗
Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians
Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’ forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians can be extracted directly from the so-obtained effective Hamiltonians. By establishing a quantitative connection between many-body states and simple models, the approach facilitates the analysis of the correlated wave functions. We propose a simple diagnostic for assessing the validity of the model space choice based on the overlaps between the target- and model-space states. Finally, artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Verification of theory on weak turbulence relating to the sequence of diffuse plasma resonances in space.
An interpretation of the sequence of diffuse plasma resonances observed by space probes (Alouette 2 and ISIS-1 satellites) is developed in terms of wave-particle nonlinear interaction in a weakly turbulent plasma including the electrostatic electron cyclotron harmonic wave instability. The longest time duration of the center frequency of the diffuse plasma resonance is found to coincide with the most favorable condition for the electrostatic electron cyclotron harmonic wave instability which is obtained by solving the dispersion equation obtained for a linear approximation of the kinetic wave equation for the warm magnetoactive plasma. The electrostatic field due to the transmission of the intense rf pulse produces plasma turbulence involving nonlinear wave-wave interaction and temperature anisotropy which leads to instability. This instability supplies energy to the turbulence. The process can be thought of as a feedback system.
Oya, H.↗
Anomalous wave structure in magnetized materials described by non-convex equations of state
We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by both the thermodynamic properties of the material and the magnetic field as well as its possible rotation. We demonstrate that phase transitions induced by material properties do not necessarily imply the loss of genuine nonlinearity of the wavefields as is the case in classical hydrodynamics. The analytical expression of the nonlinearity factor allows us to determine the specific amount of magnetic field necessary to prevent formation of complex structure induced by phase transition in the material. We illustrate our analytical approach by considering two non-convex EOS that exhibit phase transitions and anomalous behavior in the evolution. We present numerical experiments validating the analysis performed through a set of one-dimensional Riemann problems. In the examples we show how to determine the appropriate amount of magnetic field in the initial conditions of the Riemann problem to transform a thermodynamic composite wave into a simple nonlinear wave.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Higher order nonlinear equations for the dust-acoustic waves in a dusty plasma with two temperature-ions and nonextensive electrons
The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for q q{sub c}) (where q{sub c} is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Solitary waves in concentrated vortices.
A nonlinear integrodifferential equation governing finite amplitude wave propagation on concentrated vortices is solved numerically. The solution to the Cauchy problem shows a solitary wave development qualitatively similar to solutions of the Korteweg-de Vries equation. A perturbation solution of the stationary form of the evolution equation confirms the unsteady calculation.
Leibovich, S.↗
Propagation in a shearing plasma. III - Magnetic field effects and pulsar microstructure periods
Effects of a magnetic field on wave and pulse propagation in a shearing plasma are investigated. Equations for the wave fields are derived from Maxwell's equations and the Minkowski relations for an anisotropic medium, when the magnetic field is parallel to the shearing velocity. The independent propagation modes are elliptically polarized in the stationary frame and vary with the velocity of the medium. Numerical calculations are presented which show the propagation of waves and pulses through a plane-parallel shearing plasma in the case of weak and strong fields. It is found that in a weak field, propagation effects are very similar to those previously found in field-free models: the transmitted pulses acquire temporal modulations whose period is frequency dependent. In a strong field, the period of the temporal modulations is independent of frequency. Transmitted pulses can also undergo polarization changes as a result of phase differences between modes. These results are discussed in relation to their significance to propagation in a pulsar magnetosphere and, in particular, to a model for pulse microstructure.
Harding, A. K.↗
The Liouville equation for flavour evolution of neutrinos and neutrino wave packets
We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of momentum changing collisions, the LE can be reduced to a single derivative equation over a trajectory coordinate. Additional time and spatial dependence may stem from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Composite Piezoelectric Resonator 1D Modeling with Loss
Abstract – Maximizing the benefit of applying piezoelectric materials in composite structures, which are a mix of piezoelectric and elastic elements, requires analytical modeling. In this paper we describe two main classes of resonators and how to model using network equivalent including material losses. These include extensional devices where the layer areas are parallel to the direction of wave travel as found in a variety of thickness or length mode transducers (BC. Stress T1 = T2 at boundary) and transverse mode resonators (BC. Strain S1 = S2 at boundary) where the major layer area is perpendicular to the wave direction as is found in radial mode or length thickness mode composite resonators. In order to illustrate these models we will use Mason’s equivalent circuits with elastic, dielectric and piezoelectric loss. It is noted that in order to maintain consistency with the linear equations of piezoelectricity and the wave equation care is required when applying complex loss coefficients to the models. Although these techniques are applicable to other models we use Mason’s network equivalent circuit because it is intuitive for composite modeling due to the frequency independent turns ratio and the independence of the equations describing the elastic layers from the adjoining layer properties which aids in understanding the boundary conditions to impose on the layer boundaries. We will present network models for a variety of applications with loss and show how to calculate their impedance spectra, interface stress, strain velocity and displacement spectra.
Sherrit, Stewart↗
On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas
A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation of Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
General framework for calculating spin–orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions
Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner–Eckart’s theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin–orbit matrix elements by applying Wigner–Eckart’s theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born–Oppenheimer’s separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin–orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin–orbit treatment. Intrinsic issues of constructing spin–orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A numerical study of shock waves generated through laser ablation of explosives
Shock waves resulting from irradiation of energetic materials with a pulsed ultraviolet laser source have been shown to be an effective indicator for explosives detection. In this study, the features of shock wave propagation are explored theoretically. The initial stage of the shock motion is simulated as a one-dimensional process. As the nonlinear wave expands to form a blast wave, a system of conservation equations, simplified to the Euler equations, is employed to model wave propagation. The Euler equations are solved numerically by the 5th order weighted essentially non-oscillatory finite difference scheme with the time integration carried out using the 3rd order total variation diminishing Runge Kutta method. The numerical results for the shock wave evolution are compared with those obtained from experiments with a meltcast 2,6-dinitrotoluene sample. The calculations lay a theoretical foundation for a recently investigated technique for photoacoustically sensing explosives using a vibrometer.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Analysis of sound propagation in ducts using the wave envelope concept
A finite difference formulation is presented for sound propagation in a rectangular two-dimensional duct without steady flow for plane wave input. Before the difference equations are formulated, the governing Helmholtz equation is first transformed to a form whose solution does not oscillate along the length of the duct. This transformation reduces the required number of grid points by an order of magnitude, and the number of grid points becomes independent of the sound frequency. Physically, the transformed pressure represents the amplitude of the conventional sound wave. Example solutions are presented for sound propagation in a one-dimensional straight hard-wall duct and in a two-dimensional straight soft-wall duct without steady flow. The numerical solutions show evidence of the existence along the duct wall of a developing acoustic pressure diffusion boundary layer which is similar in nature to the conventional viscous flow boundary layer. In order to better illustrate this concept, the wave equation and boundary conditions are written such that the frequency no longer appears explicitly in them. The frequency effects in duct propagation can be visualized solely as an expansion and stretching of the suppressor duct.
Baumeister, K. J.↗
Three-Dimensional Navier-Stokes Simulations with Two-Equation Turbulence Models of Intersecting Shock-Waves/Turbulent Boundary Layer at Mach 8.3
An investigation of the numerical simulation with two-equation turbulence models of a three-dimensional hypersonic intersecting (SWTBL) shock-wave/turbulent boundary layer interaction flow is presented. The flows are solved with an efficient implicit upwind flux-difference split Reynolds-averaged Navier-Stokes code. Numerical results are compared with experimental data for a flow at Mach 8.28 and Reynolds number 5.3x10(exp 6) with crossing shock-waves and expansion fans generated by two lateral 15 fins located on top of a cold-wall plate. This experiment belongs to the hypersonic database for modeling validation. Simulations show the development of two primary counter-rotating cross-flow vortices and secondary turbulent structures under the main vortices and in each corner singularity inside the turbulent boundary layer. A significant loss of total pressure is produced by the complex interaction between the main vortices and the uplifted jet stream of the boundary layer. The overall agreement between computational and experimental data is generally good. The turbulence modeling corrections show improvements in the predictions of surface heat transfer distribution and an increase in the strength of the cross-flow vortices. Accurate predictions of the outflow flowfield is found to require accurate modeling of the laminar/turbulent boundary layers on the fin walls.
Bardina, J. E.↗
Numerical simulation of scattering of acoustic waves by inelastic bodies using hypersingular boundary integral equation
A numerical method for solving a problem of diffraction of acoustic waves by system of solid and thin objects based on the reduction the problem to a boundary integral equation in which the integral is understood in the sense of finite Hadamard value is proposed. To solve this equation we applied piecewise constant approximations and collocation methods numerical scheme. The difference between the constructed scheme and earlier known is in obtaining approximate analytical expressions to appearing system of linear equations coefficients by separating the main part of the kernel integral operator. The proposed numerical scheme is tested on the solution of the model problem of diffraction of an acoustic wave by inelastic sphere.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On the rogue wave propagation in ion pair superthermal plasma
Effects of superthermal electron on the features of nonlinear acoustic waves in unmagnetized collisionless ion pair plasma with superthermal electrons have been examined. The system equations are reduced in the form of the nonlinear Schrodinger equation. The rogue wave characteristics dependences on the ionic density ratio (ν = n{sub –0}/n{sub +0}), ionic mass ratio (Q = m{sub +}/m{sub −}), and superthermality index (κ) are investigated. It is worth mentioning that the results present in this work could be applicable in the Earth's ionosphere plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗