Showing papers on "Superposition principle published in 2005"

GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS: Non-Normality and Nonlinearity

Abstract: The objective of this review is to critically assess the different approaches developed in recent years to understand the dynamics of open flows such as mixing layers, jets, wakes, separation bubbles, boundary layers, and so on. These complex flows develop in extended domains in which fluid particles are continuously advected downstream. They behave either as noise amplifiers or as oscillators, both of which exhibit strong nonlinearities (Huerre & Monkewitz 1990). The local approach is inherently weakly nonparallel and it assumes that the basic flow varies on a long length scale compared to the wavelength of the instability waves. The dynamics of the flow is then considered as a superposition of linear or nonlinear instability waves that, at leading order, behave at each streamwise station as if the flow were homogeneous in the streamwise direction. In the fully global context, the basic flow and the instabilities do not have to be characterized by widely separated length scales, and the dynamics is then viewed as the result of the interactions between Global modes living in the entire physical domain with the streamwise direction as an eigendirection. This second approach is more and more resorted to as a result of increased computational capability. The earlier review of Huerre & Monkewitz (1990) emphasized how local linear theory can account for the noise amplifier behavior as well as for the onset of a Global mode. The present survey first adopts the opposite point of view by demonstrating how fully global theory accounts for the noise amplifier behavior of open flows. From such a perspective, there is strong emphasis on the very peculiar nonorthogonality of linear Global modes, which in turn allows a novel interpretation of recent numerical simulations and experimental observations. The nonorthogonality of linear Global modes also imposes severe constraints on the extension of linear global theory to the fully nonlinear regime. When the flow is weakly nonparallel, this limitation is so severe that the linear Global mode theory is of little help. It is then much more appropriate to develop a fully nonlinear formulation involving the presence of a front separating the base state region from the bifurcated state region.

A 3D photon superposition/convolution algorithm and its foundation on results of Monte Carlo calculations

Abstract: Based on previous publications on a triple Gaussian analytical pencil beam model and on Monte Carlo calculations using Monte Carlo codes GEANT-Fluka, versions 95, 98, 2002, and BEAMnrc/EGSnrc, a three-dimensional (3D) superposition/convolution algorithm for photon beams (6 MV, 18 MV) is presented. Tissue heterogeneity is taken into account by electron density information of CT images. A clinical beam consists of a superposition of divergent pencil beams. A slab-geometry was used as a phantom model to test computed results by measurements. An essential result is the existence of further dose build-up and build-down effects in the domain of density discontinuities. These effects have increasing magnitude for field sizes < or =5.5 cm(2) and densities < or = 0.25 g cm(-3), in particular with regard to field sizes considered in stereotaxy. They could be confirmed by measurements (mean standard deviation 2%). A practical impact is the dose distribution at transitions from bone to soft tissue, lung or cavities.

Method of superposition applied to patch near-field acoustic holography

Abstract: The method of superposition may be applied to reconstruct the field on a partial surface on a radiating structure from measurements made on a nearby limited surface. Unlike conformal near-field holography, where the measurement surface surrounds the entire structure, in patch holography the measurement surface need only be approximately as large as the patch on the structure surface where the reconstruction is required. Using the method of superposition, the field on and near the measurement surface may be approximated by the field produced by a source distribution placed on a surface inside the structure. The source strengths are evaluated by applying boundary conditions on the measurement surface. The algorithm requires the inversion of the Green’s function matrix which may be ill-conditioned. Truncated singular value decomposition is used to invert it. The field on the structure surface is then approximated by the field produced by the source distribution. The algorithm is easier to implement than the ...

Pair production in inhomogeneous fields

Abstract: We employ the recently developed worldline numerics, which combines string-inspired field theory methods with Monte Carlo techniques, to develop an algorithm for the computation of pair-production rates in scalar QED for inhomogeneous background fields. We test the algorithm with the classic Sauter potential, for which we compute the local production rate for the first time. Furthermore, we study the production rate for a superposition of a constant E field and a spatially oscillating field for various oscillation frequencies. Our results reveal that the approximation by a local derivative expansion already fails for frequencies small compared to the electron-mass scale, whereas for strongly oscillating fields a derivative expansion for the averaged field represents an acceptable approximation. The worldline picture makes the nonlocal nature of pair production transparent and facilitates a profound understanding of this important quantum phenomenon.

Conditional generation of arbitrary single-mode quantum states of light by repeated photon subtractions

Abstract: We propose a scheme for the conditional generation of arbitrary finite superpositions of Fock states in a single mode of a traveling optical field. The setup requires a source of squeezed vacuum states, beam splitters, strong coherent beams, photodetectors with single-photon sensitivity, and a final squeezer. If we want to generate a squeezed superposition of Fock states, which is sufficient in several applications, then the last squeezer is not even needed. The thrust of this method is that it achieves a high fidelity without requiring photodetectors with a high efficiency or a single-photon resolution. The possibility to improve its scaling by using a quantum memory is also discussed.

Synthetic-aperture imaging from high-Doppler-resolution measurements

Abstract: We develop the theory of radar imaging from data measured by a moving antenna emitting a single-frequency waveform. We show that, under a linearized (Born) scattering model, the signal at a given Doppler shift is due to a superposition of returns from stationary scatterers on a cone whose axis is the flight velocity vector. This cone reduces to a hyperbola when the scatterers are known to lie on a planar surface. In this case, reconstruction of the scatterer locations can be accomplished by a tomographic inversion in which the scattering density function is reconstructed from its integrals over hyperbolas. We give an approximate reconstruction formula and analyse the resolution of the resulting image. We provide a numerical shortcut and show results of numerical tests in a simple case.

Observation of random-phase lattice solitons

Abstract: The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or ‘discrete’) solitons1,2; these have been studied in many branches of science3,4,5,6,7,8,9,10,11. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features12. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.

Comments on "Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution

Abstract: An analytical-numerical technique, for the solution of the two-dimensional electromagnetic plane-wave scattering by a finite set of perfectly conducting circular cylinders buried in a dielectric half-space, is presented. The problem is solved for both the near- and the far-field regions, for TM and TE polarizations. The diffracted field is represented in terms of a superposition of cylindrical waves and use is made of the plane-wave spectrum to take into account the reflection and transmission of such waves by the interface. The validity of the approach is confirmed by comparisons with results available in the literature, with very good agreement. The multiple interactions between two buried cylinders have been studied by considering both the induced currents and the scattered field diagrams. Applications of the method to objects of arbitrary cross-section simulated by a suitable configuration of circular cylinders are shown.

Improving the Yule-Nielsen modified Neugebauer model by dot surface coverages depending on the ink superposition conditions

Abstract: Dot gain is different when dots are printed alone, printed in superposition with one ink or printed in superposition with two inks. In addition, the dot gain may also differ depending on which solid ink the considered halftone layer is superposed. In a previous research project, we developed a model for computing the effective surface coverage of a dot according to its superposition conditions. In the present contribution, we improve the Yule-Nielsen modified Neugebauer model by integrating into it our effective dot surface coverage computation model. Calibration of the reproduction curves mapping nominal to effective surface coverages in every superposition condition is carried out by fitting effective dot surfaces which minimize the sum of square differences between the measured reflection density spectra and reflection density spectra predicted according to the Yule-Nielsen modified Neugebauer model. In order to predict the reflection spectrum of a patch, its known nominal surface coverage values are converted into effective coverage values by weighting the contributions from different reproduction curves according to the weights of the contributing superposition conditions. We analyze the colorimetric prediction improvement brought by our extended dot surface coverage model for clustered-dot offset prints, thermal transfer prints and ink-jet prints. The color differences induced by the differences between measured reflection spectra and reflection spectra predicted according to the new dot surface estimation model are quantified on 729 different cyan, magenta, yellow patches covering the full color gamut. As a reference, these differences are also computed for the classical Yule-Nielsen modified spectral Neugebauer model incorporating a single halftone reproduction curve for each ink. Taking into account dot surface coverages according to different superposition conditions considerably improves the predictions of the Yule-Nielsen modified Neugebauer model. In the case of offset prints, the mean difference between predictions and measurements expressed in CIE-LAB CIE-94 ΔE 94 values is reduced at 100 lpi from 1.54 to 0.90 (accuracy improvement factor: 1.7) and at 150 lpi it is reduced from 1.87 to 1.00 (accuracy improvement factor: 1.8). Similar improvements have been observed for a thermal transfer printer at 600 dpi, at lineatures of 50 and 75 lpi. In the case of an ink-jet printer at 600 dpi, the mean ΔE 94 value is reduced at 75 lpi from 3.03 to 0.90 (accuracy improvement factor: 3.4) and at 100 lpi from 3.08 to 0.91 (accuracy improvement factor: 3.4).

Far-field spectral characterization of conical emission and filamentation in Kerr media

Abstract: By use of an imaging spectrometer we map the far-field (theta-lambda) spectra of 200-fs optical pulses that have undergone beam collapse and filamentation in a Kerr medium. By studying the evolution of the spectra with increasing input power and by using a model based on an asymptotic linear superposition of stationary wave modes (rather than the exact instantaneous solution), we are able to trace a consistent model of optical beam collapse highlighting the interplay between conical emission, multiple pulse splitting, and other effects such as spatial chirp.

Hydrodynamic interactions of spherical particles in suspensions confined between two planar walls

Abstract: Hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls are studied under creeping-flow conditions. The many-particle friction matrix in this system is evaluated using our novel numerical algorithm based on transformations between Cartesian and spherical representations of Stokes flow. The Cartesian representation is used to describe the interaction of the fluid with the walls and the spherical representation is used to describe the interaction with the particles. The transformations between these two representations are given in a closed form, which allows us to evaluate the coefficients in linear equations for the induced-force multipoles on particle surfaces. The friction matrix is obtained from these equations, supplemented with the superposition lubrication corrections. We have used our algorithm to evaluate the friction matrix for a single sphere, a pair of spheres, and for linear chains of spheres. The friction matrix exhibits a crossover from a quasi-two-dimensional behavior (for systems with small wall separation H) to the three-dimensional behavior (when the distance H is much larger than the interparticle distance L). The crossover is especially pronounced for a long chain moving in the direction normal to its orientation and parallel to the walls. In this configuration, a large pressure buildup occurs in front of the chain for small values of the gapwidth H, which results in a large hydrodynamic friction force. A standard wall superposition approximation does not capture this behavior.

A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solutions.

Abstract: The temporal behavior of optical response functions (ORFs) reflects the quantum dynamics of an electronic superposition state, and as such lacks a well-defined classical limit. In this paper, we consider the importance of accounting for the quantum nature of the dynamics when calculating ORFs of different types. To this end, we calculated the ORFs associated with the linear absorption spectrum and the nonlinear two-pulse photon-echo experiment, via the following approaches: (1) the semiclassical forward-backward approach; (2) an approach based on linearizing the path-integral forward-backward action in terms of the difference between the forward and backward paths; (3) an approach based on ground state nuclear dynamics. The calculations were performed on a model that consists of a two-state chromophore solvated in a nonpolar liquid. The different methods were found to yield very similar results for the absorption spectrum and “diagonal” two-pulse photon echo (i.e., the homodyne-detected signal at time t=t...

Towards quantum superpositions of a mirror: an exact open systems analysis.

Abstract: We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a nonunitary term of the Lindblad-type proportional to -[q,[q,rho]], with q the position operator for the center of mass of the mirror, and rho the statistical operator. We derive an exact formula for the fringe visibility for this system. We discuss the consequences of our result for tests of environmental decoherence and of collapse models. In particular, we find that with the conventional parameters for the continuous spontaneous localization model of state vector collapse, maintenance of coherence is expected to within an accuracy of at least 1 part in 10(8). Increasing the apparatus coupling to environmental decoherence may lead to observable modifications of the fringe visibility, with time dependence given by our exact result.

Fast and accurate calculation of physically complete EMI response by a heterogeneous metallic object

Abstract: In this paper, the coupling and close-proximity effects arising between highly conducting and permeable metallic objects are exposed and analyzed, for the electromagnetic induction (EMI) frequency range (from tens of hertz up to several hundreds of kilohertz). To understand the physics of the interaction phenomena, a numerical technique is applied, consisting of the full method of auxiliary sources (MAS) at low frequencies and a combination of the MAS with thin-skin approximation (TSA) at high frequencies. Both numerical MAS-MAS/TSA and experimental studies have shown that the scattered field from a heterogeneous target generated as a simple superposition of independent responses from each part can be very different from the field determined from whole object with full internal interaction. A new numerical technique for fast and accurate representation of EMI responses for heterogeneous objects is pursued here, applicable to any three-dimensional heterogeneous object placed in an arbitrary time-varying EMI field. First, any primary magnetic field input is decomposed into the spheroidal modes over a fictitious surface surrounding the object. Then, for each input spheroidal mode, the full EMI problem including all interaction is solved using the MAS-MAS/TSA technique, and each modal response is reproduced using a compact reduced set of sources (RSS). Finally, the total response from the given target for any other excitation can be synthesized simply by calculating that primary field's constituent spheroidal modes and combining their stored responses. Several numerical examples are designed to show how an object's electromagnetic parameters, geometry, distance between objects, antenna positions, and orientations relative to the object affect the coupling. Comparisons between numerical and measured data for a machined composite object and for an actual unexploded ordnance demonstrate the superior accuracy and applicability of the MAS-MAS/TSA RSS model over simple dipole approximations, for certain classes of heterogeneous objects.

Validation of frequency-dependent transmission line models

Abstract: The accuracy of a transmission line model can be verified by comparing its response to that by an alternative method of indisputable accuracy. This paper shows a procedure for validation which is based on the inverse Fourier transform. Desired test responses are calculated in the frequency domain using an admittance representation of the line and its terminal conditions. Time-domain step responses are calculated using the inverse Fourier transform, with semianalytic integration between sample points to permit calculation at arbitrarily large time values. The required number of frequency samples is greatly reduced by adaptively calculating the samples while considering the frequency-domain behavior of the integrand. Responses from arbitrary excitations are calculated by superposition of weighted, time-delayed step responses. The accuracy of the approach is validated for an overhead line and a cable system by comparison with responses obtained by a phase-domain line model.

Lossy transmission over slow-fading AWGN channels: a comparison of progressive and superposition and hybrid approaches

Abstract: We consider some known techniques for transmitting an analog source under the quadratic distortion criterion over a slowly-varying fading AWGN channel. We examine the case where the source is actually compressed, i.e., the source bandwidth is larger than the channel bandwidth. This makes the problem non-trivial. We optimize progressive transmission, superposition coding and an analog-digital hybrid approach in order to achieve minimal average distortion. Then, we compare the resulting optimized systems in terms of average and instantaneous reconstructed signal to noise ratio

White light propagation invariant beams.

Abstract: Propagation invariant light fields such as Bessel light beams are of interest in a variety of current areas such as micromanipulation of atoms and mesoscopic particles, laser plasmas, and the study of optical angular momentum. Considering the optical fields as a superposition of conical waves, we discuss how the coherence properties of light play a key role in their formation. As an example, we show that Bessel beams can be created from temporally incoherent broadband light sources including a halogen bulb. By using a supercontinuum source we elucidate how the beam behaves as a function of bandwidth of the incident light field.

Modeling of defect modes in photonic crystals using the fictitious source superposition method.

Abstract: We present an exact theory for modeling defect modes in two-dimensional photonic crystals having an infinite cladding. The method is based on three key concepts, namely, the use of fictitious sources to modify response fields that allow defects to be introduced, the representation of the defect mode field as a superposition of solutions of quasiperiodic field problems, and the simplification of the two-dimensional superposition to a more efficient, one-dimensional average using Bloch mode methods. We demonstrate the accuracy and efficiency of the method, comparing results obtained using alternative techniques, and then concentrate on its strengths, particularly in handling difficult problems, such as where a mode is highly extended near cutoff, that cannot be dealt with in other ways.

Excitation strategies for optical lattice microscopy

Abstract: Recently, new classes of optical lattices were identified, permitting the creation of arbitrarily large two- and three-dimensional arrays of tightly confined excitation maxima of controllable periodicity and polarization from the superposition of a finite set of plane waves. Here, experimental methods for the generation of such lattices are considered theoretically in light of their potential applications, including high resolution dynamic live cell imaging, photonic crystal fabrication, and quantum simulation and quantum computation using ultracold atoms.

Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium.

Abstract: Log-amplitude and phase-correlation and structure functions of higher-order annular laser beams in a turbulent atmosphere are derived. A higher-order annular beam source is defined as the superposition of two different higher-order Hermite-Gaussian beams. A special case of such an excitation is the annular Gaussian beam in which two beams operate at fundamental modes of different Gaussian beam sizes, yielding a doughnut-shaped (annular) beam when the second beam is subtracted from the first beam. Our formulation utilizes Rytov approximation, which makes it applicable in the weak-turbulence regime, especially for log-amplitude fluctuations. Limiting cases of our formulations correctly match with known higher-order-mode solutions that in turn reduce to the Gaussian-beam-wave (TEM00-mode) results. Our results can be applied to determine the scintillation index and the phase fluctuations in free-space optics links under higher-order annular laser beam excitation. Except for the numerical evaluation of a specific example covering an annular Gaussian beam, the results in general are left in integral form and need to be numerically evaluated in detail to obtain quantitative results.

Scattering by Buried Dielectric Cylindrical Structures

Abstract: [1] An analytical-numerical technique for the solution of the two-dimensional electromagnetic plane wave scattering by a finite set of dielectric circular cylinders buried in a dielectric half-space is presented. The problem is solved for both the near- and far-field regions, for transverse magnetic and transverse electric polarizations. The scattered field is represented in terms of a superposition of cylindrical waves, and use is made of the plane wave spectrum to take into account the reflection and transmission of such waves by the interface. The validity of the approach is confirmed by comparisons with results available in the literature, with very good agreement, and by self-consistency tests. Applications of the method to objects of arbitrary cross section simulated by suitable configurations of circular cylinders are shown.

Two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders

Abstract: The two-dimensional scattering of a Gaussian beam by a periodic array of circular cylinders is studied. The incident Gaussian beam is expressed as a superposition of plane waves of different amplitudes and different incident angles, using the plane-wave spectrum technique based on Fourier optics. For each plane wave, the scattered field is calculated with the T-matrix of an isolated circular cylinder and its lattice sums characterizing a periodic arrangement of the circular cylinders. The circular cylinders may be perfect conductors, dielectric or gyrotropic cylinders, as long as their T-matrices are known.

On the sound field of an oscillating disk in a finite open and closed circular baffle

Abstract: Equations describing the radiation characteristics of a rigid disk in a finite open baffle are derived using a method similar to that used by Streng for a circular membrane based upon the dipole part of the Kirchhoff–Helmholtz boundary integral formula. In this case, however, a power series solution to the radiation integral is derived in order to eliminate the need for numerical integration. Hence, a set of simultaneous equations is obtained by simply equating the coefficients of the power series, which leads to two mathematical functions, one real and one imaginary, that can be applied to any radial velocity distribution. This provides an alternative method to obtain the sound scattered by a disk or the complementary hole in an infinite resilient screen according to Babinet’s principle. Using the principle of superposition (or Gutin concept), it is shown how the sound radiation characteristics of a disk radiating from just one side can be obtained by combining the radiation field of a disk in a finite baffle with that of a disk in an infinite baffle. This one-sided radiator may be interpreted as a disk in a thin, circular enclosure.

A theoretical scheme for generation of nonlinear coherent states in a micromaser under intensity-dependent Jaynes-Cummings model

Abstract: In this paper we propose a theoretical scheme to show the possibility of generating various families of nonlinear (f-deformed) coherent states of the radiation field in a micromaser. We show that these states can be provided in a lossless micromaser cavity under the weak Jaynes-Cummings interaction with intensity–dependent coupling of large number of individually injected two-level atoms in a coherent superposition of the upper and lower states. In particular, we show that the so-called nonlinear squeezed vacuum and nonlinear squeezed first excited states, as well as the even and odd nonlinear coherent states can be generated in a two-photon micromaser.

Spatio-temporal vortices: properties, generation and recording

Abstract: The properties of a novel type of dislocations, called spatio-temporal vortices, are discussed. We propose to registrate them making dynamic interferogram of signal waves. Methods of their generation are suggested as well. It is illustrated that a spatio-temporal dislocation appears due to interaction of two Gauss-Laguerre pulsed beams with half-Pi phase shift. We show that superposition of two non-complanar phase modulated beams gives birth to the train of spatio-temporal vortices, which are periodical in space or time. The dynamics of a spatio-temporal vortex-soliton in defocusing Kerr-like medium is considered.

Analysis of sliding modes in the frequency domain

Abstract: A frequency-domain approach to the analysis of real and ideal sliding modes (SM) in single input single output (SISO) systems with linear plants is proposed. The real SM is analysed as a superposition of fast oscillations and slow motions in a relay system. The approach is based on the notion of the locus of a perturbed relay system (LPRS). The proposed LPRS is defined as a characteristic of the response of a linear part to an unequally spaced pulse control of variable frequency in a closed-loop. Formulas for computing the LPRS are derived. It is demonstrated that beside the well know chattering phenomenon, real SM also exhibits a non-ideal disturbance rejection, which can be quantitatively assessed with the use of the proposed approach. An example of the LPRS analysis of a SM system is given.

Generation of a superposition of multiple mesoscopic states of radiation in a resonant cavity

Abstract: Using resonant interaction between atoms and the field in a high-quality cavity, we show how to generate a superposition of many mesoscopic states of the field. We study the quasiprobability distributions and demonstrate the nonclassicality of the superposition in terms of the zeros of the Q function as well as the negativity of the Wigner function. We discuss the decoherence of the generated superposition state. We propose homodyne techniques of the type developed by [Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)] to monitor the superposition of many mesoscopic states.