Impulse Perturbations Research Articles

The quantum chaos conjecture and generalized continued fractions

The proof of the quantum chaos conjecture is given for a class of systems including as a special case the model of a rotating particle under the action of periodic impulse perturbations. (The distribution of the distances between adjacent energy levels is close to the Poisson distribution and differs from it by terms of the third order of smallness.) The proof reduces to a result in number theory on the distribution of the distances between adjacent fractional parts of values of a polynomial, while the estimate of the remainder term is based on the new theory of generalized continued fractions for vectors.

A Dynamical Mechanism for Establishing Apsidal Resonance

We show that in a system of two planets initially in nearly circular orbits, an impulse perturbation that imparts a finite eccentricity to one planet's orbit causes the other planet's orbit to become eccentric as well, and also naturally results in a libration of their relative apsidal longitudes for a wide range of initial conditions. We suggest that such a mechanism may explain orbital eccentricities and apsidal resonance in some exo-planetary systems. The eccentricity impulse could be caused by the ejection of a planet from these systems, or by torques from a primordial gas disk. The amplitude of secular variations provides an observational constraint on the dynamical history of such systems.

Surface field dynamics in dc film capacitors under an impulse voltage perturbation

For metalized polymer film capacitors, the dynamics of electric field on the electrode surface and its resulting energy dissipation influence the onset and scale of breakdown discharges within the capacitor unit, which in turn is indicative of the reliability and lifetime. To gain an understanding of the dependence of surface electric field on key system parameters, an equivalent circuit model is developed to simulate the temporal evolution of the, electric field distribution within a dc film capacitor subjected to an external impulse electric stress. A mosaic pattern of electrode segmentation is taken into account by means of an effective surface resistance and its effects on surface electric field and energy dissipation are computed numerically. Also considered are the effects of the number of electrode segments across a given length. In addition, electric energy dissipation is calculated to assess the level of possible temperature rise within the capacitor. By addressing these two issues, it is shown that the numerical code developed and its underlying methodology can serve as a complimentary tool to the present practice of capacitor designs and performance assessment.

Multicomponent adsorption equilibria from impulse response chromatography

The purpose of this work is to develop the theoretical framework of a method for obtaining multicomponent adsorption equilibrium data by dynamic, chromatographic type experiments. It is the multicomponent extension of a known principle, in use for determining single-component, and sometimes binary adsorption isotherms. It is based on analysing the response of a chromatographic column, equilibrated with a constant feed, to a small impulse perturbation of this background composition. In the single component and binary cases, a single response peak is obtained, the average exit time of which is related to the slope of the isotherm at the composition considered. In the multicomponent case, n − 1 response peaks are in general obtained, but the proper use of the information contained therein has remained an unresolved problem. In its principle, the method applies to gas-solid as well as to liquid-solid equilibria, although the experimental aspects, mainly peak detection, may be somewhat different. The development presented here is based on the following experimental procedure: a non-specific detector is used in conjunction with a conventional analytical chromatograph; n − 1 different impulse perturbations are made on the same multicomponent steady background flow, by injecting separately into the column n − 1 pure components of the mixture considered; the response to each input comprises n − 1 peaks, the average exit time and area of which are determined (first moments and zeroth partial moments of the response). In gas chromatography, a thermal conductivity detector may be used for example; in liquid chromatography, electric conductivity, UV, refractometric detection can be used, depending on the specific system. The mathematical development presented allows to work back from the experimental information to the partial derivatives of the adsorbed concentrations with respect to the fluid-phase concentrations (forming the Jacobian of the equilibria) when one non-adsorbed component is present in the mixture. The end-users procedure is particularly simple, and implies only to solve some linear equations and to invert a matrix. The procedure is then repeated for a number of discrete background compositions defining composition paths. The adsorbed-phase concentrations are obtained by numerical integration along such paths. Strategies are proposed, using straight paths through pure components, or pseudo-binary paths where only two concentrations vary; such choices allow simple boundary conditions to be used. The case where all components of the mixture are absorbed is still not completely solved in the framework of the present approach.

On the existence of absolute instability in bluff body wakes

The wake stability of steady flow past a circular cylinder has been studied experimentally. An impulse perturbation signal(very short in time, finite in amplitude) was given to the wake from a small hole on the back of the cylinder, and its long time evolution in the wake was detected by a hot film probe at a fixed point. The test Reynolds number range Re=30 ≈ 320. The result shows that (1)absolute instability exists in the wake when Re=55 ≈ 320. (2) The absolute region extends from 0.5 < ξ/ d < 0.7 ∼ 1.0 to 0.5 < ξ/ d < 2.3 ∼ 2.5 as Reyntods number increases from 55 to 200.

Mean square stability of linear dynamical systems with small Markov perturbations III. Markov impulse perturbations

Mean square stability of linear dynamical systems with small Markov perturbations III. Markov impulse perturbations

A unified approach to discretizations of the linear analysis of thermal regenerators

Two models of linear thermal regenerator operation are studied using Laplace transform techniques. It is shown that the cell model of Lai, Dudukovic and Ramachandran and the trapezoidal rule discretization of Hill and Willmott are related by changes of time scale and parameters. A matrix formalism is developed for representing transient regenerator operation. The formalism is used to elucidate the physical interpretation of the equations for the cyclic steady state, and to study heat recovery following an impulse perturbation to the gas inlet temperature. The ultimate fractional heat recovery from such a perturbation can be found from the cyclic steady state outlet gas dimensionless temperature distribution; it is bounded by the maximum and minimum values of that distribution.

Comparison methods for impulsively perturbed delay-differential control systems

Until recently most authors have devoted their research to the theory of functional differential systems with continuous perturbation. A very general comparison theorem for functional differential systems with impulse perturbation is developed employing the theory of systems functional differential inequalities. Sufficient conditions are given to insure that the solutions are integrally stable.

Periodic solutions of quasilinear non‐autonomous systems with impulses

AbstractThe paper considers a system of differential equations with impulse perturbations at fixed moments in time of the formmagnified imagewhere x ϵ Rn, ε is a small parameter,Sufficient conditions have been found for existence of the periodic solution of the given system in the critical and non‐critical cases.

Periodic solutions of quasilinear non-autonomous systems with impulses

The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the formwhere x ∈ Rn, ε is a small parameter,Sufficient conditions are found for the existence of the periodic solution of the given system in the critical and non-critical cases.

INTEGRAL SURFACES FOR HYPERBOLIC ORDINARY DIFFERENTIAL EQUATIONS WITH IMPULSES

The paper considers integral surfaces of systems of differential equations with impulse perturbations at fixed moments of time. Sufficient conditions have been obtained for the existence of integral surfaces with definite properties and the behaviour of the solutions has been studied with initial conditions outside these surfaces.

Time‐dependent density operator in the random impulse approximation: I. Connections with the “generalized sudden approximation” for photoionization and electron impact ionization; and II. Relevance to reduced density operators, particle–hole matrices, and propagators for the initial state

AbstractA density operator analysis is made of the particle‐ejection (e.g., photoionization) problem in the “generalized sudden approximation” for the case in which the ejected particle is detected but its dynamical properties are not observed. It is shown that the resultant statistical density operator may be derived from that obtained in a particle‐conserving Hamiltonian‐evolution linear‐response model with a random impulse perturbation, and that the physical applicability of the latter model embraces the range of applicability of the former. The initial value of the statistical density operator for the above particle‐ejection problem is shown to be the N – (1)‐particle reduced density operator of the initial state; and the initial value of the statistical density operator for the excitations in the random impulse model is shown to be the N‐particle Hermitian operator whose matrix representation is the G matrix of Garrod and Percus. The significance of the eigenvalue spectrum of these operators to the excitation properties of the system is discussed, especially for the random impulse model, where a large eigenvalue of the G matrix can signal strong preferential excitation to its corresponding particle‐hole collective state, even for a random perturbation. Extensions of these ideas to excitations from states with a large eigenvalue of the two‐particle reduced density operator (e.g., superconducting states) are mentioned. The The applicability of these density matrices to the description of the excitation spectrum due to a well‐defined perturbation is discussed. The relationship of these time‐dependent density operators to the one‐particle propagator and the particle–hole propagator (polarization propagator) is established.

Analysis of the relaxation response induced by various forms of pulse perturbation of coupled chemical equilibria

Abstract In transient relaxation method studies of fast reactions, if the rate of response of the chemical system is comparable with that of the perturbation, the exact shape of the forcing function must be taken into account in the kinetic treatment of the relaxation response. An analysis of the transient response of multiple coupled equilibria using Laplace transform is presented for various forms of step or impulse perturbation. The method enables one to calculate the relaxation amplitudes for an unrestricted number of coupled chemical equilibria. Various aspects of the analysis of the relaxation response are discussed.

Penetration of Boundary Perturbations in Unstable Chemical Systems

The effects of boundary perturbations of chemical species are investigated in a linear analysis for systems of coupled chemical reactions, with diffusion, which have instabilities. At marginal stability of one of the harmonic modes of such a system the penetration depth of the chemical boundary perturbation coupled to that mode approaches infinity at resonance, that is, at the frequency of boundary perturbation equal to the marginal oscillatory frequency of the mode. For the case of equal and diagonal diffusion coefficients for all chemical species the penetration of the perturbation is homogeneous at resonance. In general inhomogeneous penetration occurs in association with symmetry-breaking instabilities of the system. The propagation of an impulse boundary perturbation is derived. Some possible applications of the theory are suggested but not demonstrated: (1) analysis of chemical instabilities; (2) analogies of electronic devices such as tuned amplifiers, transmitters, and receivers (chemical radio); (3) communication in aggregates of biological systems; and (4) mechanism of pheromone emission and reception.

Ionic forces and membrane phenomena

When a membrane containing diffusible ions is perturbed by an electric field, osmotic and electric relaxation forces are developed. These are calculated for an infinitesimal impulse perturbation. The force characteristics are dependent on the shape of the fixedcharge distribution. The electric force is proportional to the concentration difference, while the osmotic force is proportional to the second derivative of the chemical potential. The residual electric field gives rise to membrane reactance. With two diffusible cations having different concentrations and mobilities, two decaying potential terms are obtained. Under certain conditions these may be represented as due to a real RLC electric circuit. If the mobility of a diffusible cation varies in the membrane, it is possible for the osmotic force to cancel the electric. The case is examined for mobility inversely proportional to the negative fixed charge density, and the requisite charge distribution calculated. It appears that this effect may be of importance in explaining the activity of the axonal membrane. Boundary forces are examined in detail in the Appendices, including the effect of lack of equilibrium. Force relationships are calculated for the uniform fixed-charge membrane.