Showing papers on "Superposition principle published in 2011"
TL;DR: This paper introduces a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and proves that the method does indeed succeed in decomposing arbitrary functions in this class.
1,704 citations
TL;DR: A linear superposition principle of exponential traveled waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves.
Abstract: A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3+1 dimensional KP, Jimbo-Miwa and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is also raised and discussed about generating Hirota bilinear equations possessing the indicated N-wave solutions, and a few illustrative examples are presented, together with an algorithm using weights.
374 citations
TL;DR: It is demonstrated that a structured light intensity pattern can be produced at the output of a multi-mode optical fiber by shaping the wavefront of the input beam with a spatial light modulator.
Abstract: We demonstrate that a structured light intensity pattern can be produced at the output of a multi-mode optical fiber by shaping the wavefront of the input beam with a spatial light modulator. We also find the useful property that, as in the case for free space propagation, output intensities can be easily superimposed by taking the argument of the complex superposition of corresponding phase-only holograms. An analytical expression is derived relating output intensities ratios to hologram weights in the superposition.
232 citations
TL;DR: In this paper, the authors investigated the nature of a walker's wave field and found that it is formed by the superposition of waves emitted by the droplet collisions with the interface.
Abstract: On a vertically vibrating fluid interface, a droplet can remain bouncing indefinitely. When approaching the Faraday instability onset, the droplet couples to the wave it generates and starts propagating horizontally. The resulting wave–particle association, called a walker, was shown previously to have remarkable dynamical properties, reminiscent of quantum behaviours. In the present article, the nature of a walker's wave field is investigated experimentally, numerically and theoretically. It is shown to result from the superposition of waves emitted by the droplet collisions with the interface. A single impact is studied experimentally and in a fluid mechanics theoretical approach. It is shown that each shock emits a radial travelling wave, leaving behind a localized mode of slowly decaying Faraday standing waves. As it moves, the walker keeps generating waves and the global structure of the wave field results from the linear superposition of the waves generated along the recent trajectory. For rectilinear trajectories, this results in a Fresnel interference pattern of the global wave field. Since the droplet moves due to its interaction with the distorted interface, this means that it is guided by a pilot wave that contains a path memory. Through this wave-mediated memory, the past as well as the environment determines the walker's present motion.
166 citations
TL;DR: The explicit form of the spin-orbit interaction (SOI) with the inertial effects due to the mechanical rotation is presented and equations of motion for a wave packet of electrons in two-dimensional planes subject to the SOI are derived.
Abstract: We study the Pauli-Schrodinger equation in a uniformly rotating frame of reference to describe a coupling of spins and mechanical rotations. The explicit form of the spin-orbit interaction (SOI) with the inertial effects due to the mechanical rotation is presented. We derive equations of motion for a wave packet of electrons in two-dimensional planes subject to the SOI. The solution is a superposition of two cyclotron motions with different frequencies and a circular spin current is created by the mechanical rotation. The magnitude of the spin current is linearly proportional to the lower cyclotron frequency.
125 citations
TL;DR: In this article, a single microwave photon is prepared in a superposition of two states of different frequency using a superconducting quantum interference device to mediate the coupling between two harmonics.
Abstract: A single microwave photon is prepared in a superposition of two states of different frequency. This is achieved by using a superconducting quantum interference device to mediate the coupling between two harmonics of a superconducting resonator.
103 citations
TL;DR: In this paper, the topology of composite flowfields reconstructed by linear superposition of the two-dimensional flow around a stalled airfoil and the leading stationary three-dimensional global eigenmode has been studied.
Abstract: Critical point theory asserts that two-dimensional topologies are defined as degeneracies and any three-dimensional disturbance of a two-dimensional flow will lead to a new three-dimensional flowfield topology, regardless of the disturbance amplitude. Here, the topology of the composite flowfields reconstructed by linear superposition of the two-dimensional flow around a stalled airfoil and the leading stationary three-dimensional global eigenmode has been studied. In the conditions monitored the two-dimensional flow is steady and laminar and is separated over a fraction of the suction side, while the amplitudes considered in the linear superposition are small enough for the linearization assumption to be valid. The multiple topological bifurcations resulting have been analysed in detail; the surface streamlines generated by the leading stationary global mode of the separated flow have been found to be strongly reminiscent of the characteristic stall cells, observed experimentally on airfoils just beyond stall in both laminar and turbulent flow.
100 citations
TL;DR: In this article, an aberration compensation method using superposition imaging and inexpensive postprocessing is proposed, where the focusing distance and optical axis position of an imaging system with aberrations are varied over certain ranges, and the resulting images are superposed to equalize the point spread function within a three-dimensional region and remove space variance.
Abstract: In this paper, we propose an aberration compensation method using superposition imaging and inexpensive postprocessing. In the method, the focusing distance and optical axis position of an imaging system with aberrations are varied over certain ranges, and the resulting images are superposed to equalize the point spread function (PSF) within a three-dimensional region and remove space variance. A sharp image of an object with a large depth-of-field and field-of-view is then reconstructed by deconvolution of the superposed image using the effective three-dimensionally space-invariant PSF. The effectiveness of the proposed method was verified by simulations assuming defocus, the five Seidel aberrations, and vignetting.
99 citations
TL;DR: In this paper, the problem of generating discrete superpositions of coherent states in the process of light propagation through a nonlinear Kerr medium, which is modelled by the anharmonic oscillator, is discussed.
Abstract: The problem of generating discrete superpositions of coherent states in the process of light propagation through a nonlinear Kerr medium, which is modelled by the anharmonic oscillator, is discussed. It is shown that under an appropriate choice of the length (time) of the medium the superpositions with both even and odd numbers of coherent states can appear. Analytical formulae for such superpositions with a few components are given explicitly. General rules governing the process of generating discrete superpositions of coherent states are also given. The maximum number of well distinguished states that can be obtained for a given number of initial photons is estimated. The quasiprobability distribution $Q(\alpha,\alpha^*,t)$ representing the superposition states is illustrated graphically, showing regular structures when the component states are well separated.
98 citations
TL;DR: FastMag as mentioned in this paper is a fast micromagnetic simulator for general problems that solves the Landau-Lifshitz-Gilbert equation and can handle multiscale problems with a high computational efficiency.
Abstract: A fast micromagnetic simulator (FastMag) for general problems is presented FastMag solves the Landau–Lifshitz–Gilbert equation and can handle multiscale problems with a high computational efficiency The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel graphics processing unit (GPU) architectures FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular Thus, discretized superposition integrals are computed using a nonuniform grid interpolation method, which evaluates the field from N sources at N collocated observers in O(N) operations This approach allows h
80 citations
TL;DR: A theoretical understanding of the source of the compression-only behavior of oscillating phospholipid-coated ultrasound contrast agent microbubbles is provided through a weakly nonlinear analysis of the shell buckling model proposed by Marmottant et al.
Abstract: Oscillating phospholipid-coated ultrasound contrast agent microbubbles display a so-called “compression-only” behavior, where it is observed that the bubbles compress efficiently while their expansion is suppressed. Here, a theoretical understanding of the source of this nonlinear behavior is provided through a weakly nonlinear analysis of the shell buckling model proposed by Marmottant et al. [J. Acoust. Soc. Am. 118, 3499–3505 (2005)]. It is shown that the radial dynamics of the bubble can be considered as a superposition of a linear response at the fundamental driving frequency and a second-order nonlinear low-frequency response that describes the negative offset of the mean bubble radius. The analytical solution deduced from the weakly nonlinear analysis shows that the compression-only behavior results from a rapid change of the shell elasticity with bubble radius. In addition, the radial dynamics of single phospholipid-coated microbubbles was recorded as a function of both the amplitude and the frequency of the driving pressure pulse. The comparison between the experimental data and the theory shows that the magnitude of compression-only behavior is mainly determined by the initial phospholipids concentration on the bubble surface, which slightly varies from bubble to bubble
TL;DR: The possibility of diagnostics of optical currents in liquids caused by polarization characteristics of an optical field alone, using nanoscale metallic particles has been shown experimentally and the prospects of studying temporal coherence using the proposed approach are made.
Abstract: We present the computer simulation results of the spatial distribution of the Poynting vector and illustrate motion of micro and nanoparticles in spatially inhomogeneously polarized fields. The influence of phase relations and the degree of mutual coherence of superimposing waves in the arrangements of two-wave and four-wave superposition on the characteristics of the microparticle’s motion has been analyzed. The prospects of studying temporal coherence using the proposed approach are made. For the first time, the possibility of diagnostics of optical currents in liquids caused by polarization characteristics of an optical field alone, using nanoscale metallic particles has been shown experimentally.
01 Jan 2011
TL;DR: A fast micromagnetic simulator (FastMag) for general problems is presented, which solves the Landau-Lifshitz-Gilbert equation and can handle problems of a small or very large size with a high speed.
Abstract: A fast micromagnetic simulator (FastMag) for general problems is presented. FastMag solves the Landau-Lifshitz-Gilbert equation and can handle problems of a small or very large size with a high speed. The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel Graphics Processing Unit (GPU) architectures. FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems. The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain. This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular. Thus discretized superposition integrals are computed using a non-uniform grid interpolation method, which evaluates the field from N sources at N collocated observers in ( ) O N operations. This approach allows handling any uniform or non-uniform shapes, allows easily calculating the field outside the magnetized domains, does not require solving linear system of equations, and requires little memory. FastMag is implemented on GPUs with GPU-CPU speed-ups of two orders of magnitude. Simulations are shown of a large array and a recording head fully discretized down to the exchange length, with over a hundred million tetrahedral elements on an inexpensive desktop computer.
TL;DR: In this paper, an analytical method is derived for determining the vibrations of two plates which are generally supported along the boundary edges, and elastically coupled together at an arbitrary angle by four types of coupling springs of arbitrary stiffnesses.
Patent•
05 Jul 2011
TL;DR: In this article, the bits of information are divided into a first part representing a predetermined number of bits and a second part representing the output of the corresponding encoding circuits with the parts provided to the respective encoding circuits and their outputs combined by a superposition.
Abstract: A communication system uses a bus to transmit information, by receiving signals and mapping them to a second set of signals representing codewords of a superposition signaling code, and transmitting the second set of signals. The superposition signaling code can comprise more than one layer. The pin-efficiency can be larger than 1. The system may encode bits into a codeword of a superposition signaling code that is defined by two basis vectors of predetermined size and then have two encoders for permutation modulation codes defined by the basis vectors. The bits of information are divided into a first part representing a predetermined number of bits and a second part representing a predetermined number of bits, with the parts provided to the respective encoding circuits and their outputs combined by a superposition.
TL;DR: In this paper, the phase sensitive superposition of different plasmonic modes leads to a spatially controllable enhancement of the near-field inside and in the vicinity of a metallic nanostructure.
Abstract: We show experimentally as well as in simulation that the phase-sensitive superposition of different plasmonic modes leads to a spatially controllable enhancement of the near-field inside and in the vicinity of a metallic nanostructure. Multiphoton photoemission electron microscopy maps the local near-field distribution. By controlling the relative phase $\ensuremath{\Theta}$ between two orthogonally polarized light pulses the spatial distribution of the near-field is manipulated on the basis of the interference of the near-field modes. This demonstration of optical near-field control is corroborated by finite integral time domain calculations.
TL;DR: The findings provide a systematic framework for designing far-field and near-field experiments to drive multipole transitions and provide information on molecular structure that is inaccessible to other spectroscopic techniques and open the possibility for new types of optical control of molecules.
Abstract: Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the fields and field gradients at a single point in space. Many configurations cannot be generated from a single plane wave, regardless of polarization, but any allowed configuration can be generated by superposition of multiple plane waves. There is no local configuration of the fields and gradients that requires near-field effects. Second, we derive a set of local electromagnetic quantities, each of which couples to a particular multipole transition. These quantities are small or zero in plane waves, but can be large in regions of certain superpositions of plane waves. Our findings provide a systematic framework for designing far-field and near-field experiments to drive multipole transitions. The proposed experiments provide information on molecular structure that is in...
TL;DR: In this article, the authors combine a more efficient representation of finite-length sources in terms of components related to the wire and its end points with very general expressions for EM fields in 1D layered media.
Abstract: In present-day land and marine controlled-source electromagnetic (CSEM) surveys, electromagnetic fields are commonly generated using wires that are hundreds of metres long. Nevertheless, simulations of CSEM data often approximate these sources as point dipoles. Although this is justified for sufficiently large source-receiver distances, many real surveys include frequencies and distances at which the dipole approximation is inaccurate. For 1D layered media, electromagnetic (EM) fields for point dipole sources can be computed using well-known quasi-analytical solutions and fields for sources of finite length can be synthesized by superposing point dipole fields. However, the calculation of numerous point dipole fields is computationally expensive, requiring a large number of numerical integral evaluations. We combine a more efficient representation of finite-length sources in terms of components related to the wire and its end points with very general expressions for EM fields in 1D layered media. We thus obtain a formulation that requires fewer numerical integrations than the superposition of dipole fields, permits source and receiver placement at any depth within the layer stack and can also easily be integrated into 3D modelling algorithms. Complex source geometries, such as wires bent due to surface obstructions, can be simulated by segmenting the wire and computing the responses for each segment separately. We first describe our finite-length wire expressions and then present 1D and 3D examples of EM fields due to finite-length sources for typical land and marine survey geometries and discuss differences to point dipole fields.
TL;DR: In this paper, the biphoton state generated by spontaneous parametric down-conversion in a thin crystal and under collinear phase matching conditions using a pump consisting of any superposition of Laguerre-Gauss modes was calculated.
Abstract: We calculate the biphoton state generated by spontaneous parametric down-conversion in a thin crystal and under collinear phase matching conditions using a pump consisting of any superposition of Laguerre-Gauss modes. The result has no restrictions on the angular or radial momenta or, in particular, on the width of the pump, signal and idler modes. We demonstrate the strong effect of the ratio of the pump width to the signal/idler widths on the composition of the down-converted entangled fields. The knowledge of this ratio is shown to be essential for calculating the maximally entangled states that can be produced using pumps with a complex spatial profile.
TL;DR: In this article, a mathematically rigorous technique was proposed for the optimization of various optical properties of electromagnetic fields in free space and including scattering interactions, where the linearity of the electromagnetic fields along with the quadratic nature of the intensity were exploited to define specific optical Eigenmodes (OEi) that are pertinent to the interaction considered.
Abstract: We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields in free space and including scattering interactions. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of the intensity to define specific Optical Eigenmodes (OEi) that are pertinent to the interaction considered. Key applications include the optimization of the size of a focused spot, the transmission through sub-wavelength apertures, and of the optical force acting on microparticles. We verify experimentally the OEi approach by minimising the size of a focused optical field using a superposition of Bessel beams.
TL;DR: This spin to orbital angular momentum conversion provides a new method for the generation and annihilation of optical vortices in an all-optical arrangement that is solely dependent on the incident polarisation and vortex handedness.
Abstract: Internal conical diffraction produces a superposition of orthogonally polarised zero- and first-order Bessel like beams from an incident circularly polarised Gaussian beam For right-circularly polarised light, the first-order beam has an optical vortex of charge -1 Upon propagation of the first-order beam through a second biaxial crystal, a process which is termed cascade conical refraction, the generated beam is a superposition of orthogonally polarised fields of charge 0 and -1 or 0 and -2 This spin to orbital angular momentum conversion provides a new method for the generation and annihilation of optical vortices in an all-optical arrangement that is solely dependent on the incident polarisation and vortex handedness
TL;DR: In this article, a new analytical method for springback of small curvature plane bending is addressed with unloading rule of classical elastic-plastic theory and principle of strain superposition.
Abstract: A new analytical method for springback of small curvature plane bending is addressed with unloading rule of classical elastic-plastic theory and principle of strain superposition. We start from strain analysis of plane bending which has initial curvature, and the theoretic derivation is on the widely applicable basic hypotheses. The results are unified to geometry constraint equations and springback equation of plane bending, which can be evolved to straight beam plane bending and pure bending. The expanding and setting round process is one of the situations of plane bending, which is a bend-stretching process of plane curved beam. In the present study, springback equation of plane bending is used to analyze the expanding and setting round process, and the results agree with the experimental data. With a reasonable prediction accuracy, this new analytical method for springback of plane bending can meet the needs of applications in engineering.
TL;DR: A comprehensive, GPU-accelerated dose engine in order to provide a substantial performance gain over CPU based implementations and introduce the concepts of arc superposition and delta superposition.
Abstract: Purpose: To accelerate dose calculation to interactive rates using highly parallel graphics processing units (GPUs). Methods: The authors have extended their prior work in GPU-accelerated superposition/convolution with a modern dual-source model and have enhanced performance. The primary source algorithm supports both focused leaf ends and asymmetric rounded leaf ends. The extra-focal algorithm uses a discretized, isotropic area source and models multileaf collimator leaf height effects. The spectral and attenuation effects of static beam modifiers were integrated into each source's spectral function. The authors introduce the concepts of arc superposition and delta superposition. Arc superposition utilizes separate angular sampling for the total energy released per unit mass (TERMA) and superposition computations to increase accuracy and performance. Delta superposition allows single beamlet changes to be computed efficiently. The authors extended their concept of multi-resolution superposition to include kernel tilting. Multi-resolution superposition approximates solid angle ray-tracing, improving performance and scalability with a minor loss in accuracy. Superposition/convolution was implemented using the inverse cumulative-cumulative kernel and exact radiological path ray-tracing. The accuracy analyses were performed using multiple kernel ray samplings, both with and without kernel tilting and multi-resolution superposition. Results: Source model performance was <9 ms (data dependent) for a high resolution (400{sup 2})more » field using an NVIDIA (Santa Clara, CA) GeForce GTX 280. Computation of the physically correct multispectral TERMA attenuation was improved by a material centric approach, which increased performance by over 80%. Superposition performance was improved by {approx}24% to 0.058 and 0.94 s for 64{sup 3} and 128{sup 3} water phantoms; a speed-up of 101-144x over the highly optimized Pinnacle{sup 3} (Philips, Madison, WI) implementation. Pinnacle{sup 3} times were 8.3 and 94 s, respectively, on an AMD (Sunnyvale, CA) Opteron 254 (two cores, 2.8 GHz). Conclusions: The authors have completed a comprehensive, GPU-accelerated dose engine in order to provide a substantial performance gain over CPU based implementations. Real-time dose computation is feasible with the accuracy levels of the superposition/convolution algorithm.« less
TL;DR: In this paper, a pump-probe scheme for preparing and monitoring electron-nuclear motion in a dissociative coherent electronic-nuclear wave packet is explored from numerical solutions of a non-Born-Oppenheimer time-dependent Schrodinger equation.
Abstract: A pump-probe scheme for preparing and monitoring electron-nuclear motion in a dissociative coherent electron-nuclear wave packet is explored from numerical solutions of a non-Born-Oppenheimer time-dependent Schr\"odinger equation. A mid-ir intense few-cycle probe pulse is used to generate molecular high-order-harmonic generation (MHOHG) from a coherent superposition of two or more dissociative coherent electronic-nuclear wave packets, prepared by a femtosecond uv pump pulse. Varying the time delay between the intense ir probe pulse and the uv pump pulse by a few hundreds of attoseconds, the MHOHG signal intensity is shown to vary by orders of magnitude, thus showing the high sensitivity to electron-nuclear dynamics in coherent electron-nuclear wave packets. We relate this high sensitivity of MHOHG spectra to opposing electron velocities (fluxes) in the electron wave packets of the recombining (recolliding) ionized electron and of the bound electron in the initial coherent superposition of two electronic states.
TL;DR: In this paper, a comprehensive study of magnetohydrodynamic (MHD) waves and instabilities in a weakly ionized system, such as an interstellar molecular cloud, is presented, and all the critical wavelengths of perturbations across which the sustainable wave modes can change radically (and so can their decay rates).
Abstract: We present a comprehensive study of magnetohydrodynamic (MHD) waves and instabilities in a weakly-ionized system, such as an interstellar molecular cloud. We determine all the critical wavelengths of perturbations across which the sustainable wave modes can change radically (and so can their decay rates), and various instabilities are present or absent. Hence, these critical wavelengths are essential for understanding the effects of MHD waves (or turbulence) on the structure and evolution of molecular clouds. Depending on the angle of propagation relative to the zeroth-order magnetic field and the physical parameters of a model cloud, there are wavelength ranges in which no wave can be sustained as such. Yet, for other directions of propagation or different properties of a model cloud, there may always exist some wave mode(s) at all wavelengths (smaller than the size of the model cloud). For a typical model cloud, magnetically-driven ambipolar diffusion leads to removal of any support against gravity that most short-wavelength waves (or turbulence) may have had, and gravitationally-driven ambipolar diffusion sets in and leads to cloud fragmentation into stellar-size masses, as first suggested by Mouschovias more than three decades ago - a single-stage fragmentation theory of star formation, distinct from the then prevailing hierarchical fragmentation picture. The phase velocities, decay times and eigenvectors (e.g. the densities and velocities of neutral particles and the plasma, and the three components of the magnetic field) are determined as functions of the wavelength of the disturbances in a mathematically transparent way and are explained physically. Comparison of the results with those of nonlinear analytical or numerical calculations is also presented where appropriate, excellent agreement is found, and confidence in the analytical, linear approach is gained to explore phenomena difficult to study through numerical simulations. Mode splitting (or bifurcation) and mode merging, which are impossible in single-fluid systems for linear perturbations (hence, the term 'normal mode' and the principle of superposition), occur naturally in multifluid systems (as do transitions between wave modes without bifurcation) and have profound consequences in the evolution of such systems.
23 Feb 2011
TL;DR: In this paper, a brief history of Cavitation and Ultrasound is outlined and acknowledgements stress, strain and elasticity are discussed. And the Uniform State of Stress Stress on an Inclined Plane Transformation of Stress for Rotation of Axes Principle Stress Stationary Values of Sheet Stress Octahedral Stresses Hydrostatic (Dilational) and Deviatoric Stress Tensors Strains and Displacements General Hooke's Law Equilibrium Equations for Three Dimensions Strain Compatibility Equations Plane Strain Plane Stress Polar Coordinates Stress Functions Stress Functions in Polar
Abstract: Introduction Definition of Sound A Brief History of Cavitation and Ultrasound Outline and Acknowledgements Stress, Strain and Elasticity The Uniform State of Stress Stress on an Inclined Plane Transformation of Stress for Rotation of Axes Principle Stress Stationary Values of Sheet Stress Octahedral Stresses Hydrostatic (Dilational) and Deviatoric Stress Tensors Strains and Displacements General Hooke's Law Equilibrium Equations for Three Dimensions Strain Compatibility Equations Plane Strain Plane Stress Polar Coordinates Stress Functions Stress Functions in Polar Coordinates Vibrations Mass on a Spring Free Vibrations Damped Free Vibrations Forced Vibrations Undamped Forced Vibrations Damped Forced Vibrations Nonlinear Springs Waves and Sound Wave Equation Speed of Sound in Air Solutions of the 1-Dimensional Wave Equation Sound Energy Point and Line Sources Doppler Effect Root-Mean-Square Pressure Superposition of Waves Beats Complex Representation of a Plane, Harmonic Wave Standing Wave Fourier Transform Decibel Scale Vectorial Notation for the Wave Equation Plane Waves in Isotropic Media Waves in Fluids Mechanisms of Attenuation Reflection and Transmission Scattering Nonlinear Propagation Transducers The Piezo-Effect Piezo Electric Materials Transducer Bandwidth Transducer Construction Radiated Fields Continuous Wave Excitation Transient Excitation Focussing Transducer Arrays Medical Imaging Standard Ultrasonic Imaging Modes Doppler Methods Special Techniques Artefacts Biological Effects of Ultrasound and Safety Regulations Bubble Physics Hollow Sphere Cavitation Threshold Fundamental Equation of Bubble Dynamics Pressure Radiated by a Bubble Viscous Fluids Oscillations Disruption Diffusion Radiation Forces Coalescence Jetting CEUS and Sonoporation Commercial Ultrasound Contrast Agents CEUS Some Non-Cardiac Imaging Applications Molecular Imaging Increased Drug Uptake Causes of Sonoporation Drug Carriers Gene Delivery Therapeutic News Anitbubbles Cell Death High-Intensity Focussed Ultrasound Concluding Remarks
TL;DR: In this article, a new method for the calibration of arrays is presented that allows the simultaneous calibration of N array elements, which comprises the measurement of the array output signal at M phase settings applied to the N elements involved in the calibration.
Abstract: A new method for the calibration of arrays is presented that allows the simultaneous calibration of N array elements. It comprises the measurement of the array output signal at M phase settings applied to the N elements involved in the calibration. These M phase settings correspond to a linear phase taper that is unique for each of the involved elements and reveals therefore N different phase tapers. The complex M measurements of the array signal are thought to be the excitation coefficients of a synthetic M -element linear phased array. The array factor of this synthetic M-element array comprises a superposition of N+1 array factors all pointing with their main beam into different directions. By converting this superposition of N+1 array factors into a set of N+1 simultaneous linear equations, the signals of the N individual elements to be calibrated including the combined signal contribution of the static elements, can be solved by standard matrix inversion techniques. Computer simulations are presented to demonstrate the capabilities of the new calibration method.
TL;DR: In this paper, the virtual wave source method (VWSM) is adopted to take account of multiple wave reflections among joints, and a comparison between results from VWSM and those from the method of characteristics (MC) is carried out.
TL;DR: This work describes a new procedure to obtain optimal molecular superposition based on quantum similarity (QS): the geometric‐quantum similarity molecularsuperposition (GQSMS) algorithm, inspired by the QS Aufbau principle.
Abstract: This work describes a new procedure to obtain optimal molecular superposition based on quantum similarity (QS): the geometric-quantum similarity molecular superposition (GQSMS) algorithm. It has been inspired by the QS Aufbau principle, already described in a previous work, to build up coherently quantum similarity matrices (QSMs). The cornerstone of the present superposition technique relies upon the fact that quantum similarity integrals (QSIs), defined using a GTO basis set, depend on the squared intermolecular atomic distances. The resulting QSM structure, constructed under the GQSMS algorithm, becomes not only optimal in terms of its QSI elements but can also be arranged to produce a positive definite matrix global structure. Kruskal minimum spanning trees are also discussed as a device to order molecular sets described in turn by means of QSM. Besides the main subject of this work, focused on MS and QS, other practical considerations are also included in this study: essentially the use of elementary Jacobi rotations as QSM refinement tools and inward functions as QSM scaling methods.
TL;DR: Large-time behavior of solutions to the inflow problem of full compressible Navier–Stokes equations is investigated, and the asymptotic stability of the superposition of the above four wave patterns is proven under some smallness conditions.
Abstract: Large-time behavior of solutions to the inflow problem of full compressible Navier–Stokes equations is investigated on the half line $\mathbf{R}_+=(0,+\infty)$. The wave structure, which contains four waves—the transonic (or degenerate) boundary layer solution, the 1-rarefaction wave, the viscous 2-contact wave, and the 3-rarefaction wave to the inflow problem—is described, and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier–Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the treatments of the degeneracies in the transonic boundary layer solution and the wave interactions in the superposition wave.