Resonance Approximation Research Articles

Static pressure and temperature coefficients of laboratory standard microphones

The sensitivity of condenser measurement microphones depends on the environmental conditions due to the changes in the acoustic properties of the enclosed air between diaphragm and backelectrode and in the cavity behind the backelectrode. A theoretical investigation has been performed based on an extended lumped parameter representation of the mechanical and acoustical elements of the microphone, assuming the velocity distribution of the diaphragm to follow the zero-order Bessel function. The extension involves the frequency dependency of the dynamic diaphragm mass and stiffness as well as a first-order approximation of resonances in the back cavity. It was found that each of the coefficients, for a given type of microphone, can be expressed by a single function when the coefficients are normalized by their low-frequency value and the frequency axis normalized by the individual resonance frequency of the microphone. The static pressure and temperature coefficients were determined experimentally for about 20 samples of type BK 4160 and BK 4180 microphones. The results agree almost perfectly with the predictions for BK 4160, while some modifications of the lumped parameter values are called for to make the results for BK 4180 fit the predicted values.

One method of describing the transfer of energy of the kinetic degrees of freedom to the electronic states of molecules

An analysis is made of the process of transferring the kinetic energy of highly excited vibrational terms of a molecule to an electronic state of one of its constituent atoms. This is done by utilizing a wave equation for the effective wave functions of the atom, corresponding to mixed states, in which the velocity of this atom relative to the neighboring atoms in the molecule enters as a parameter. An expression is found for the excitation probability in the case of a hydroge-like atom in the resonant approximation.

Equation of State of the Classical Charged Particles

The equilibrium behavior of the three-dimensional (3D) classical charged particles moving in a homogeneous background is investigated by using a modified cluster integral expansion method. A partial summation of the multi-loop diagrams is applied to extending the equation of state to the next order beyond the ring approximation.

Density of states in the Drude–Lorentz model of a nonpolar fluid

The frequency-dependent self-susceptibility of a selected particle in the Drude–Lorentz model of a nonpolar fluid is shown to have a universal absorption spectrum in the limit of low density. We derive an expression for the universal lineshape and calculate the limit function by a scaling procedure, in a self-consistent ring approximation. The line shape is found to be an asymmetric function of frequency, as suggested by computer simulation data for systems of hard spheres and of atoms with Lennard-Jones interactions. A calculation of correction terms accounting for the effect of the microstructure at moderate density leads to fairly good agreement with existing computer simulation data.

Quantum and classical chaos in a thin film (heterostructure) in a tilted magnetic field

Classical and quantum dynamics of a spinless charged particle moving in a thin film placed in a tilted magnetic field is investigated. In the classical limit, nonlinear resonances and the condition of stochastization (Chirikov criterion) are studied. In the quantum case, a system of interacting resonances and an isolated resonance are analyzed. The energy spectrum is calculated numerically in the resonance approximation, and the statistics of the interlevel intervals is examined.

Quantum cyclotron resonance in a degenerate system. Quasienergetic states

We study the quantum dynamics of a charged particle rotating in a constant magnetic field and in the field of a monochromatic wave propagating perpendicular to the magnetic field under the condition of cyclotron resonance. Quasienergies and quasienergy functions are numerically calculated in the resonance approximation. The passage to the limit from the quantum model to the classical one is discussed.

Fine-Structure Resolved Dielectronic Recombination Rates for the N = 3 Excited Configurations of Fe xvi--Fe XIX

view Abstract Citations (7) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Fine-Structure Resolved Dielectronic Recombination Rates for the N = 3 Excited Configurations of Fe XVI--Fe XIX Dasgupta, Arati Abstract Spectroscopic analysis of X-ray emission lines from hot astrophysical plasmas, such as solar and cosmic X-ray sources, is a powerful tool in the determination of elemental abundances and temperature and density diagnostics of the emitting gas. This same analysis can be used to model high-temperature laboratory plasmas associated with magnetic and inertial confinement fusion as well as with the study of X-ray laser research. Accurate determination of atomic rates is crucial for a reliable analysis. Dielectronic recombination is the dominant recombination process for incompletely ionized plasmas. The rate coefficients for dielectronic recombination of several ionization stages of the astrophysically abundant element iron (Fe xvi-Fe xi x) are presented at the fine-structure levels of the n = 3 excited states at several temperatures. The rate coefficients are calculated for a Maxwellian electron distribution in a low-density corona approximation. The dielectronic recombination process involves a large number of doubly excited states of the recombined ions and computations of many radiative as well as autoionization rates from these states. In this calculation we include doubly excited states that are formed by the free electron captured up to very high Rydberg states and detailed calculations of all possible dipole allowed radiative transitions and all dipole as well as nondipole autoionization transitions. Transitions to excited states of the recombining ion from all open autoionization channels, which have a significant effect in reducing the rate coefficients (as presented in the works of Jacobs et al.), are also included in our calculations. These calculations were carried out in the isolated resonance approximation using the Hartree-Fock method with relativistic corrections (as described by Cowan). The dielectronic recombination rate coefficients were evaluated at many temperatures encompassing the range around the temperature of maximum abundance. These J-resolved data will be extremely useful for accurate ionization balance calculations for astrophysical as well as laboratory iron plasmas. Publication: The Astrophysical Journal Supplement Series Pub Date: December 1995 DOI: 10.1086/192247 Bibcode: 1995ApJS..101..401D Keywords: ATOMIC DATA; ATOMIC PROCESSES; X-RAYS: GENERAL full text sources ADS |

Electric-field enhancement of dielectronic recombination from a continuum of finite bandwidth.

A small electric field is shown to increase the dielectronic recombination, via autoionizing Rydberg states, of an electron from a continuum of finite bandwidth. The continuum of finite bandwidth is a broad autoionizing state which is part of a series converging to a higher limit, and the field enhancement of the rate occurs because the field converts the nl Rydberg states to nk Stark states, increasing the number of contributing recombination paths. The experimental results are in excellent agreement with the predictions of an isolated resonance approximation treatment and show clearly both the positive effect of Stark mixing and the negative effect of field ionization on dielectronic recombination.

Robust Control of Uncertain Resonant Systems

This work deals with the control synthesis of resonant systems. In this work we present a new resonance approximation which enables efficient calculation of closed loop properties at resonant frequencies. The approximation is used to accommodate low damping resonances in a QFT design procedure. The extended design procedure is applied to the solution of the benchmark problem: ‘robust digital control of a flexible transmission’. The results offer insight to the fundamental tradeoffs of single input single output resonant system design.

Spin-isospin response functions and the effects of the Delta -hole configurations in finite nuclei.

Effects of the delta-isobar ([Delta]) mixing on the spin-isospin response functions in finite nuclei are studied in the quasielastic region. A method to calculate the response function for a finite system composed of nucleon ([ital N]) and [Delta] is formulated in a ring approximation. It is designed to treat the [Delta]-related Landau-Migdal parameters [ital g][sub [ital N][Delta]][sup [prime]], [ital g][sub [Delta][Delta]][sup [prime]] and the nucleon parameter [ital g][sub [ital N][ital N]][sup [prime]], independently, so that the universality ansatz, [ital g][sub [ital N][ital N]][sup [prime]]=[ital g][sub [ital N][Delta]][sup [prime]]=[ital g][sub [Delta][Delta]][sup [prime]], is removed. We calculated the isovector spin-longitudinal and -transverse response functions, [ital R][sub [ital L]] and [ital R][sub [ital T]], with and without the [Delta] mixing. Inclusion of [Delta] enhances [ital R][sub [ital L]] but reduces [ital R][sub [ital T]] for ordinary interactions. Dependence of [ital R][sub [ital L],][ital T] on [ital g][sub [ital N][ital N]][sup [prime]] and [ital g][sub [ital N][Delta]][sup [prime]] is investigated. Decomposition into the process-decomposed response functions, [ital R][sup [[ital N][ital N]]], [ital R][sup [[ital N][Delta]]], and [ital R][sup [[Delta][Delta]]], is very elucidative to see the [Delta] effects, which are found to be mainly governed by [ital R][sup [[ital N][Delta]]] and sensitive to [ital g][submore » [ital N][Delta]][sup [prime]]. The isovector spin-transverse response function [ital R][sub [ital T]][sup ([ital e],][ital e][sup [prime])] obtained by ([ital e],[ital e][prime]) is calculated by various effective interactions and compared to each other as well as experimental data.« less

Diffusion in lattice Lorentz gases with mixtures of point scatterers.

Monte Carlo simulations are carried out to evaluate the diffusion coefficient in some lattice Lorentz gases with mixtures of point scatterers in the limit of a low concentration of scatterers. Two models on a square lattice are considered: (a) right and left stochastic rotators plus pure reflectors and (b) right and left stochastic mirrors plus pure reflectors. The simulation data are compared with the repeated ring approximation (RRA). The agreement is excellent for models in the absence of pure reflectors, suggesting that the RRA gives the correct diffusion coefficient for those cases. As the fraction [ital x][sub [ital B]] of reflectors increases, the diffusion coefficient decreases and seems to vanish at [ital x][sub [ital B]][sup [ital c]][congruent]0.8 (percolation threshold) with a critical exponent [mu][congruent]2 (stochastic model) or [mu][congruent]3 (deterministic rotator model).

Buckling of thick orthotropic cylindrical shells under external pressure based on non-planar equilibrium modes

A formulation based on the three dimensional theory of elasticity is employed to study the buckling of an orthotropic cylindrical shell under external pressure. In this paper, a non-zero axial displacement and a full dependence of the buckling modes on the three coordinates is assumed, as opposed to the ring approximation employed in the earlier studies. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko non-shallow shell formulations. Two cases of end conditions are considered; one with both ends of the shell fixed, and the other with both ends capped and under the action of the external pressure. Moreover, two cases of orthotropic material are considered with stiffness constants typical of glass/epoxy and graphite/epoxy. For the isotropic material case, the predictions of the simplified (single expression) Donnell and the Flügge and the Danielson and Simmonds theories are also compared. In all cases, the elasticity approach predicts a lower critical load than the shell theories, the percentage reduction being larger with increasing thickness. The degree of non-conservatism depends strongly on the material properties, being smaller for the isotropic case. Furthermore, although it is a commonly accepted notion that the critical point in loading under external pressure occurs for n = 2 and m = 1 (number of circumferential waves and number of axial half-waves, respectively), it was found that this is not the case for the strongly orthotropic graphite/epoxy material and the moderately thick construction; for this case, the value of m at the critical point is greater than 1 (yet, in all cases n = 2).

Relation between the landing-launching coefficient and the attenuation of surface waves propagating around an elastic cylindrical object

One approach for developing a physical understanding of the scattering of sound from elastic objects in water is to use the Sommerfeld–Watson transformation (SWT). Following the works of Überall etal., it is known that elastic objects resonances are due to a phase matching of the surface waves propagating around the scatterer. What is more, resonance widths are related to surface waves attenuation, thereby showing the close link between resonance and surface waves propagation phenomena. According to the geometrical theory of diffraction, surface waves are also characterized by a landing coefficient and a launching one, both identical in the present case. This landing–launching coefficient calculated from the SWT gives an indication, as resonance widths and surface waves attenuation, on the coupling between the object and the surrounding fluid. The purpose of this work is to determine an analytical relation between the landing–launching coefficient and the attenuation of surface waves. This relation comes from an identification between the Breit–Wigner approximation of resonances and the Mittag–Leffler expansions related to surface waves contribution. Thereafter, a method of identification of the background introduced by Flax etal. in the acoustic scattering theory has been developed.

Resonant magnetopolaron effects in parabolic quantum wells: Perpendicular magnetic field

The energy of magnetopolaron levels is calculated at the resonance of the first excited level with the ground-state level plus one longitudinal-optical phonon for a parabolic quantum well using an improved resonance approximation. The degeneracy between these levels is lifted by the electron-phonon interaction and the levels are resonance split. It is shown by numerical calculations that the renormalization of the levels Δ E ± above and below the crossing energy depends strongly on the confinement energy of the parabolic potential. We obtain analytic results for the energy shifts Δ E ± in the limits of two-dimensional (2D) and three-dimensional (3D) resonant magnetopolarons.

Resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field

We study the resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field. The renormalization of the first excited level, which is resonant with the ground state level plus one longitudinal-optical phonon is calculated at the resonance using an improved resonance approximation to be ΔE=γαβ where α is the polaron coupling constant. The exponent β and the factor γ are calculated in dependence on the tilt angle of the magnetic field and the confinement energy.

A stochastic model of the Earth-Moon tidal evolution accounting for cyclic variations of resonant properties of the ocean: an asymptotic solution

A stochastic model of the Earth-Moon tidal evolution taking into account fluctuating effects of the continental drift is described. The above effects caused by alternation of periods of consolidation and disintegration of continents are specified as a combination of cyclic variations and superimposed random perturbations of the ocean eigenoscillation spectrum. The solution is found with use of one-mode and multi-mode resonance approximations. In other words, we assume that the ocean response to the Moon's forcing is due to one or several resonant modes predominant over all other ocean eigenoscillations. For the multi-mode resonance approximation, the model ensures a proper time scale of the Earth-Moon tidal evolution and qualitative agreement of predicted changes in the number of solar days and synodic months per year with paleontological and sedimentological data. Moreover, it makes possible fitting of model estimates of tidal energy dissipation to those derived from global paleotide models for different periods of the Phanerozoic.

Effect of interference of quantum states on the broadening of energy levels in a strong electromagnetic field

The wave equation, written down for ψ-functions averaged over the gauge, is solved within the resonance approximation for a number of low levels of a hydrogen-like atom, located in a strong electromagnetic field and undergoing impact action. It is shown that the interference of quantum states, resulting from the interaction of the atom with its surrounding, may lead, depending on the conditions, to a further dependence of the broadening or narrowing of spectral line contours on the external field intensity.

Collective diffusion in a lattice gas automaton

We report on non-mean-field and ring-kinetic-theory calculations of both the momentum autocorrelation function and the collective diffusion coefficient in a diffusive lattice gas automaton. For both quantities the ring approximation is calculated exactly. A saddle point method yields a leadingt−2 and a subleadingt−5/2 long-time tail in the momentum autocorrelation function. The ring kinetic corrections to the mean field value of the diffusion coefficient are in good agreement with computer simulations.

Statistical mechanics of vortex system in a thin-film superconductor in the ring approximation

The statistical mechanics and thermodynamics of a two-dimensional system of vortices in a thin superconducting film are constructed. The long-range interaction of the vortices is taken into account in the ring approximation well known from plasma theory.

Self-consistent ring approximation in quantum hadrodynamics

Within the framework of quantum hadrodynamics including Δ-baryons we sum up all ring diagrams in a self-consistent method which is developed as a generalization of the Hartree-Fock approximation. We can demonstrate analytically by using the Källén-Lehmann representation for the polarization propagator that the ring-energy contributions are purely real under assumptions which we show to be well fulfilled. The resulting equation of state becomes soft compared to the Hartree-Fock result with an incompressibility of κ ≈ 200–350 MeV, and the effective mass increases to M ∗ M ≈ 0.8 . Following the practice in mean-field and Hartree-Fock calculations so far, we regard the theory as an effective one, and drop all divergent parts of the loop diagrams.