Showing papers on "Superposition principle published in 1992"

Entangled coherent states

Abstract: The nonlinear Mach-Zehnder interferometer is presented as a device whereby a pair of coherent states can be transformed into an entangled superposition of coherent states for which the notion of entanglement is generalized to include nonorthogonal, but distinct, component states. Each mode is directed to a homodyne detector. We show that there exist nonclassical intensity correlations at the output ports of the homodyne detectors which facilitate a test of local realism. In contradistinction to previous optical schemes which test local realism, the initial state used here possesses a positive Glauber-Sudarshan representation and is therefore a semiclassical state. The nonlinearity itself is responsible for generating the nonclassical state.

Superpositions of coherent states: Squeezing and dissipation

Abstract: In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.

Interrelation between continuous and discrete relaxation time spectra

Abstract: A relation has been derived between the continuous and the discrete forms of linear viscoelastic relaxation-time spectra. Both forms can be interconverted, and they are equivalent in their ability to reproduce G′(ω), G″(ω), or G(t) data. The linear superposition of even only a few Maxwell-modes is able to mimic the continuous form. This rapid conversion leads to the ‘parsimonious’ spectrum which models the linear viscoelastic relaxation with the smallest possible number of modes. Typical experimental spectra of broadly distributed and of monodisperse polymers provide the means for testing the proposed relations. Effects of noise and data density were studied for G′, G″-data sets.

A new impedance spectrometer for the investigation of electrochemical systems

Abstract: The development of a computer‐controlled electrochemical impedance spectrometer, based on a Fourier transform algorithm is described. Together with a fast potentiostat the system can be used in the frequency range 1 mHz to 100 kHz. The perturbation signal is a superposition of sine waves with properly chosen frequencies. The overall measurement time is limited only by the lowest frequency in the spectrum and by the data transfer to the computer, thus, time‐resolved impedance spectra measurements can be performed. The principle of operation and technical details are presented and discussed.

Diffraction impulse response of rectangular transducers

Abstract: A closed‐form expression for the impulse velocity potential of rectangular pistonlike transducers, without any far field or paraxial approximation, is presented. The classical time‐domain impulse response approach is used considering free‐field, rigid baffle, and pressure release boundary conditions. Previous approaches to the rigid baffled rectangular piston require the use of superposition methods in order to find a general solution numerically. These must add or subtract, according to the field point location, the analytical expressions that were derived only for specific field points or geometrical regions. In this paper the complexity introduced by the geometrical discontinuities of rectangular apertures is analyzed. A new compacting methodology is proposed and applied to obtain a general solution for the impulse response. This new solution provides the value of the impulse response directly in the time domain, without requiring superposition methods. In addition, a closed‐form solution for the pressure impulse response is also presented. This can be useful for physical insight and a qualitative analysis of transient and continuous wave pressure fields. Also included is a description of the temporal behavior of the impulse velocity potential and the pressure impulse response for field points in different regions. The proposed solution allows an efficient and accurate computation of pressure fields under realistic excitations. Several examples illustrate the use of this new solution in the computation of transient pressure waveforms, when wideband and relatively narrow‐band excitation pulses are used. Three‐dimensional plots of the peak amplitude of the transient pressure near field are presented, and certain characteristics are analyzed using the pressure impulse response.

Schrödinger-cat states at finite temperature : influence of a finite-temperature heat bath on quantum interferences

Abstract: Recently several methods have been proposed for generation of superposition (Schrodinger-cat) states in microwave cavities. At microwave frequencies, thermal photons can significantly affect statistical properties of superposition states. In the present paper we study the influence of a thermal heat bath on nonclassical properties of quantum superposition states

Interference of diffusive light waves.

Abstract: We examine interference effects resulting from the superposition of photon-density waves produced by coherently modulated light incident upon a turbid medium Photon-diffusion theory is used to derive expressions for the ac magnitude and phase of the aggregate diffusive wave produced in full- and half-space volumes by two sources Using a frequency-domain spectrometer operating at 410 MHz, we verify interference patterns predicted by the model in scattering samples having optical properties similar to those of skin tissue Potential imaging applications of interfering diffusive waves are discussed in the context of the theoretical and experimental results

Two-mode nonclassical state via superpositions of two-mode coherent states.

Abstract: The superposition states from several two-mode coherent states are studied. It is shown that under certain conditions the superposition states may exhibit nonclassical effects, such as two-mode squeezing, violation of the Cauchy-Schwartz inequality, and sub-Poissonian statistics.

The wave superposition method as a robust technique for computing acoustic fields

Abstract: The wave superposition method has recently been advocated [Koopmann et al., ‘‘A method for computing acoustic fields based on the principle of wave superposition,’’ J. Acoust. Soc. Am. 86, 2433–2438 (1989)], as a reliable and accurate technique for computing the acoustic fields generated by arbitrary‐shaped radiators; this study examines in depth the robustness and numerical stability of the method. The implementation of the method requires the placement of a finite number of point sources on a surface interior to the body of the radiator. The magnitude of these point sources can be evaluated in terms of the prescribed velocity distribution on the surface of the radiator. Once calculated, the magnitude of these point sources allow the pressure distribution exterior to the radiator to be evaluated. The first improvement made to the robustness of the method is the use of a hybrid combination of monopole and dipole sources; this modification allows the inherent problem of nonuniqueness of the method at certa...

Superposition in Infiltration Modeling

Abstract: Simplified, physical models for calculating infiltration and ventilation in a single zone usually calculate the airflows from the two natural driving forces (i.e., wind and stack effects) separately, and then use a superposition rule to combine them. Similarly, superposition rules may be used to ascertain the effects of mechanical systems on infiltration. In this report a general superposition rule will be derived for combining wind, stack, and mechanical ventilation systems together. The superposition rule will be derived using general principles of leakage dismbution and airflow and will not depend on the details of a particular infiltration model. In the process of generating this rule, a quantity called leakage distribution angle is developed to quantify the separation of areas of the building envelope which are subject to infiltration and exfiltration. The general superposition rule is compared to other proposed superposition rules including those based on measured data, and the general rule is shown to have strong explanatory power Results are generated for typical buildings. The concept of fan addition efficency is developed to determine the effectiveness of unbalanced (mechanical) ventilation systems at augmenting infiltration.

A numerical model for wave scattering problems in infinite media due to p‐ and sv‐wave incidences

Abstract: Based on elastic wave motion theory and the superposition concept, a numerical model for wave scattering problems in infinite media due to P-wave and SV-wave incidences is presented in this paper. Since this model is based on a coupled system of finite and infinite elements for simulating wave propagation in infinite media, the complexity of geometry and the variability of material properties in the foundation can be realistically simulated. Through a systematic study of the characteristics of a plane harmonic P-wave and SV-wave incidences on a fixed boundary, the concept of stress increase factors and stress factors which can be used to calculate the generalized stresses on the wave input boundary due to the SV-wave and P-wave incidences is also proposed. The effects of incident wave mode, incident angle and Poisson's ratio in the foundation on the stress increase factors and the stress factors have been studied in detail. Finally, the proposed model has been applied to a half-plane foundation and a semi-circular canyon to calculate SV-wave and P-wave scattering problems. The numerical results obtained show good agreement with the theoretical results and Wong's analytical results.

Amplitude preprocessing of single and multicomponent seismic data

Abstract: Whenever the data acquisition is restricted to line surveys rather than areal surveys, seismic processing is necessarily in two dimensions. In this paper it is argued that two-dimensional (2-D) processing is preferably applied after transforming the point source responses into line source responses. The effect of this transformation is a correction of the amplitudes in the data. For single-component acoustic data as well as for multicomponent elastic data a line source response is nothing but a superposition of point source responses. Hence, in principle a line source response can be synthesized by integrating point source responses along the desired line source axis. In practice, however, this integration cannot be carried out due to the incompleteness of the data. It is shown that the integration along the source axis can be replaced by an integration along the receiver axis. The underlying assumption is that the wavefields exhibit a certain type of cylindrical symmetry. For horizontally layered acoustic and elastic media this assumption is fully satisfied. For 2-D inhomogeneous media this assumption is approximately satisfied, provided the data are sorted in CMP gathers. Having transformed the point source responses into line source responses, the results may be considered as 'true amplitude' 2-D data. Hence, proceeding with existing 2-D seismic processing techniques is then justified.

Simulations to demonstrate reduction of the Gordon–Haus effect

Abstract: The superposition of spontaneous emission noise on a train of soliton pulses produces a random change of the center frequency of the soliton spectrum that causes a change of the group velocity of individual solitons, which in long-light-wave systems translates into a random jitter of the position of the pulses at the receiver. This phenomenon is known as the Gordon-Haus effect. If uncontrolled, the Gordon-Haus effect sets a definite limit on the permissible data rate or on the length of soliton-based light-wave systems. Recently Kodama and Hasegawa [Opt. Lett. 17, 31 (1992)] have shown that the Gordon-Haus effect can be suppressed by placing filters along the fiber that reduce the frequency jitter and the concomitant group-velocity changes. We demonstrate the reduction of the Gordon-Haus effect by computer simulations.

Spectral Analysis of Wave Motion in Plane Solids With Boundaries

Abstract: A spectral formulation is employed whereby in-plane stress waves are synthesized from the superposition of components at discrete frequencies and wavenumbers. The summations are performed using the fast Fourier transform and the Fourier series, respectively. Because the components are discrete, the solution to problems (over the entire field) with completely arbitrary loading, both in time and space, is made tractable. Waves generated from a line load acting on an infinite and semiinfinite plane are first considered. A cascade approach is then adopted for the treatment of these waves incident on a free, fixed, and elastic boundary. At each stage, the results are compared with those obtained from the available classical solutions and/or finite element results. These studies will form the basis for the investigation of in-plane stress waves in multiply layered media.

Preparation and detection of macroscopic quantum superpositions by two-photon field-atom interactions.

Abstract: We put forward a simple, feasible scheme for the preparation and subsequent detection of macroscopic quantum superposition (MQS) states. It is based on the two-photon model which obtains when a cascade of two atomic transitions is resonant with twice the field frequency. The initial conditions amount to a field in a mixed state characteristic of lasers or masers and an excited atom. The MQS is generated by a conditional measurement of the atomic excitation after an interaction time that determines the relative phase of the MQS components. Remarkably, the MQS is subsequently detected and its phase is inferred by measuring the excitation probability of a second, ``probe,'' atom, as a function of its interaction time. The realization of the scheme in the optical domain, using dielectric microspheres, is discussed.

Finite-amplitude waves in deformed mooney-rivlin materials

Abstract: In a previous paper (3), Currie and Hayes showed that two linearly polarized finite-amplitude shear waves, polarized in directions orthogonal to each other and to the direction of propagation n, may propagate along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation.Here, we recover this result and obtain explicit expressions for the speeds of the two waves in terms of the angles that n makes with special directions, called 'acoustic axes'. These are the only directions such that the two wave speeds are equal. They are determined only by the basic static deformation of the material. There are two such directions if this deformation is triaxial, and one if it is biaxial.Then, it is shown that, although the theory is nonlinear, the superposition of the two waves propagating along any direction is also a solution. In particular, for propagation along an acoustic axis, elliptically and circularly polarized finite-amplitude waves are possible.Finally, the energy flux and energy density of the waves are considered. © 1992 Oxford University Press.

A new algorithm to calculate the transient near-field of ultrasonic phased arrays

Abstract: An algorithm valid for an accurate calculation of the near-field in the scanning plane of ultrasonic phased arrays is presented. Using the classical time-domain impulse response approach, a simple analytical expression for the impulse response at points lying in the central plane of a narrow rectangular aperture is decided. An expression for the array impulse response is then obtained by superposition. The proposed solution is useful for an efficient computation of transient and continuous wave (CW) pressure fields without requiring any far-field or paraxial approximations. Moreover, the convolution-impulse response approach applied to phased arrays constitutes an important tool for the analysis of array fields. Some numerical examples are presented, in which the advantages of using the array impulse response in the field analysis are shown. Several aspects of array fields not currently described in literature are included in the examples. >

Stochastic fluid analysis of an ATM multiplexer loaded with heterogeneous ON-OFF sources: an effective computational approach

Abstract: The authors study the loss performance of an asynchronous transfer mode (ATM) multiplexer, whose input consists of the superposition of a multiplicity of heterogeneous on-off sources. The stochastic fluid flow approach yields the entire buffer occupancy probability distribution in terms of the solution of a linear differential equation system. The focus is on the numerical investigation of the steady-state behavior of models involving very large state spaces. A novel approximate technique is introduced allowing a dramatic reduction of the computational burden, so that the analysis of a large variety of traffic mixes becomes feasible. Many numerical results are presented to support the accuracy of the method. Applications of the analysis method are outlined. >

Improved Fixed Interface Method for Modal Synthesis

Abstract: The paper takes a fresh look at the important topic of substructure synthesis. An improved technique for synthesizing the modes obtained with fixed interface coordinates is proposed. The reduction in the size of a substructure model is achieved through a higher order mode superposition approach. For the first time, an analytical rationale for the popular Craig-Bampton-Hurty method is presented. It is shown that the CraigBampton-Hurty method is a special case of the proposed method. The proposed approach can be used to improve the accuracy of the calculated eigenproperties by utilizing the higher order component modes but without calculating additional normal modes of the substructures. Numerical results are presented to demonstrate the effectiveness of the proposed method with the increasing order of the mode superposition approach used. The approach is expected to be efficient if the degrees of freedom at the interface of the substructures are relatively small compared with the degrees of freedom of the substructures.

True three-dimensional dose computations for megavoltage x-ray therapy: a role for the superposition principle.

Abstract: The objective of radiation therapy is to concentrate a prescribed radiation dose accurately within a target volume in the patient. Major advances in imaging technology have greatly improved our ability to plan radiation treatments in three dimensions (3D) and to verify the treatment geometrically, but there is a concomitant need to improve dosimetric accuracy. It has been recommended that radiation doses should be computed with an accuracy of 3% within the target volume and in radiosensitive normal tissues. We review the rationale behind this recommendation, and describe a new generation of 3D dose algorithms which are capable of achieving this goal. A true 3D dose calculation tracks primary and scattered radiations in 3D space while accounting for tissue inhomogeneities. In the past, dose distributions have been computed in a 2D transverse slice with the assumption that the anatomy of the patient dose not change abruptly in nearby slices. We demonstrate the importance of computing 3D scatter contributions to dose from photons and electrons correctly, and show the magnitude of dose errors caused by using traditional 2D methods. The Monte Carlo technique is the most general and rigorous approach since individual primary and secondary particle tracks are simulated. However, this approach is too time-consuming for clinical treatment planning. We review an approach that is based on the superposition principle and achieves a reasonable compromise between the speed of computation and accuracy in dose. In this approach, dose deposition is separated into two steps. Firstly, the attenuation of incident photons interacting in the absorber is computed to determine the total energy released in the material (TERMA). This quantity is treated as an impulse at each irradiated point. Secondly, the transport of energy by scattered photons and electrons is described by a point dose spread kernel. The dose distribution is the superposition of the kernels, weighted by the magnitude of the TERMA impulse for all interaction sites. In this review, we demonstrate the capabilities of the superposition method, particularly for situations of charged particle disequilibrium, and we report on the progress made by several research groups in adapting this method to clinical treatment planning. In the future, the superposition method will have a significant role in dose optimization for conformal irradiation techniques because of its close correspondence to image reconstruction by filtered back-projection.

Transient Analysis of a Semi-infinite Crack Subjected to Dynamic Concentrated Forces

Abstract: An exact transient closed-form solution for a semi-infinite crack subjected to a time-dependent concentrated force is obtained in this study. The total wave field is due to the effect of this point source and the scattering of the incident waves by the crack tip. An alternative methodology for constructing the reflected and diffracted field is proposed, which proves both powerful and efficient in solving complicated dynamic crack problems. An exponentially distributed loading at the crack surfaces in the Laplace transform domain is used as the fundamental problem. The waves reflected by the traction-free crack surface and diffracted from the crack tip can be constructed by superimposing this fundamental solution. The superposition is per­formed in the Laplace transform domain. Numerical results for the time history of stresses and stress intensity factors during the transient process are obtained and compared with the corresponding static values. It is shown that the field solution will approach the static value after the last diffracted wave has passed. 1 Introduction The interaction of a stress wave with a crack in an unbounded medium is a complicated problem. The incident wave will be reflected by the crack surface and diffracted from the crack tip. The analytical study of this problem is restricted to rela­tively simple cases. The investigation of transient elastody-namic crack problem was studied by de Hoop (1958) who analyzed the response of applying uniform normal pressure on the surfaces of a semi-infinite crack. Handelman and Rubenfeld (1969) investigated the reflection and diffraction of a horizontally polarized plane shear wave by a semi-infinite crack. Thau and Lu (1971) studied the diffraction of an incident longitudinal plane wave disturbed by a crack of finite length. They did not solve this problem completely. They used a so­lution to a semi-infinite crack to track the waves from one crack tip to the other, and stopped after one interaction. These problems were solved using the method of integral transforms together with the application of Wiener-Hopf technique (Noble, 1958) and Cagniard-de Hoop method (de Hoop, 1958) of Laplace inversion. Because there is no characteristic length involved, the integral transform can be applied directly and the standard Wiener-Hopf equation can be obtained. In a series of papers, Freund (1972a, 1972b, 1973, 1974a) developed im­portant analytical methods for evaluating the transient field of a propagating crack. In Freund's papers, a fundamental