Scattering Amplitudes Research Articles

A MUSIC Algorithm for Locating Small Inclusions Buried in a Half-Space from the Scattering Amplitude at a Fixed Frequency

In this paper a MUSIC (standing for multiple signal classification) algorithm for locating small inclusions buried in a half-space from the scattering amplitude at a fixed frequency is developed. The underlying application area which motivated this work is the imaging of antipersonnel mines from electromagnetic data, formulated as an inverse scattering problem for the Helmholtz equation. The algorithm makes use of an asymptotic expansion of the scattering amplitude. A derivation of the leading-order term in this asymptotic expansion and its application for designing a MUSIC type of algorithm are presented. The viability of this algorithm is documented by a variety of numerical results.

Two Numerical Methods for Recovering Small Inclusions from the Scattering Amplitude at a Fixed Frequency

In this paper two noniterative algorithms for locating small electromagnetic inclusions from the scattering amplitude at a fixed frequency are developed. In particular, a variety of numerical results is presented to highlight their potential and their limitations.

Funktionelle Cine-MRT des Kolon: Darstellung und Quantifizierung der Darmmotilität

To develop and evaluate a method to visualize and quantify large bowel motility using functional cine MRI. Fifteen healthy individuals (8 males, 7 females, 20 to 45 years old) with no history or present symptoms of bowel disorders were enrolled in a functional cine MRI examination at 6 a. m. after a starving phase for at least eight hours before and after oral administration of Senna tea (mild stimulating purgative). Two consecutive sets of repeated measurements of the entire abdomen were performed using a 1.5 T MRI system with coronal T2-weighted HASTE sequences anatomically adjusted to the course of the large bowel. A navigator technique was used for respiratory gating at the level of the right dorsal diaphragm. The changes in diameter (given in cm) were measured at 5 different locations of the ascending (AC), transverse (TC) and descending colon (DC), and assessed as parameters for the bowel motility. The mean values as a statistical measure for large bowel relaxation were determined. Before ingestion of Senna tea, the mean diameter measured 3.41 cm (ascending colon), 3 cm (transverse colon) and 2.67 cm (descending colon). After the ingestion of Senna tea, the mean diameter increased to 3.69 cm (ascending colon) to 3.4 cm (transverse colon) and to 2.9 cm (descending colon). A statistically significant difference was demonstrated with the Wilcoxon test (level of confidence 0.05). For the determination of dynamic increase, the changes of the statistical scatter amplitude to the mean value were expressed as percentage before and after the ingestion of Senna tea. Thereby, an increase in variation and dynamic range was detected for the AC (112.9 %) and DC (100 %), but a decrease in the dynamics for the TC (69 %). A non-invasive method for the assessment of bowel motility was developed for the first time. The use of functional cine MRI utilizing a prokinetic stimulus allowed visualisation and quantification of large bowel motility. Further studies have to determine whether this technique is clinically relevant.

Calculation of Zero-Norm States and Reduction of Stringy Scattering Amplitudes

We give a simplified method to generate two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. Zero-norm states up to the fourth massive level and general formulas of some zero-norm tensor states at arbitrary mass levels are calculated. On-shell Ward identities generated by zero-norm states and the factorization property of stringy vertex operators can then be used to argue that the string-tree scattering amplitudes of the degenerate lower spin propagating states are fixed by those of higher spin propagating states at each fixed mass level. This decoupling phenomenon is, in contrast to Gross’s high-energy symmetries, valid to all energies. As examples, we explicitly demonstrate this stringy phenomenon up to the fourth massive level (spin-five), which justifies the calculation of two other previous approaches based on the massive worldsheet sigma-model and Witten’s string field theory (WSFT).

Radiation belt electron precipitation fluxes associated with lightning

In this study we consider the dependence of precipitation fluxes arising from whistler‐induced radiation belt losses on the strength of the associated lightning's return stroke current. As a result of this work, it will be possible to use lightning activity data sets to estimate globally induced precipitation flux rates and thus determine the lightning‐induced effect on the radiation belts more accurately. Four study days were selected, during which a high proportion of the lightning activity occurring near the east coast of North America produced observable Trimpi effects on VLF transmitter signals propagating in the region of the Antarctic Peninsula (∼L = 2–2.5). The lack of lightning in Antarctica gives this location a unique advantage for this study. The functional dependence of the relative scattered field amplitude with the return stroke peak current of the lightning discharge suggests that during these events diffusion conditions are occurring near the precipitating radiation belt particles loss cone due to strong whistler wave fields, probably caused by ducted signals. The range of observed Trimpi scatter amplitude of −10 to −35 dB was produced by precipitation bursts with energy fluxes estimated to range over 6.5–0.4 × 10−3 ergs cm−2 s−1. The largest fluxes were found to be driven by lightning currents of about 250 kA, while the smallest detectable fluxes relate to lightning currents of 70 kA. Although 3 of the 4 study days showed a high degree of consistency between the levels of lightning return stroke peak current required to produce any given perturbation scatter amplitude value, conditions were significantly different on 23 April 1994. On this day, observed Trimpi signatures were 6–7 dB greater for any given lightning intensity than on the other study days. These events are consistent with a significantly harder radiation belt precipitation spectra, probably caused by geomagnetic storm‐time acceleration processes of radiation belt electrons.

Nonperturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations

We here use our nonperturbative, cluster decomposable relativistic scattering formalism to calculate photon–spinor scattering, including the related particle–antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it a unitary two-particle amplitude for quantum–particle scattering. We verify that we have done this correctly by showing that our calculated photon–spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.

MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos

The Cachazo-Svrcek-Witten approach to perturbative gauge theory is extended to gauge theories with quarks and gluinos. All googly amplitudes with quark-antiquark pairs and gluinos are computed and shown to agree with the previously known results. The computations of the non-MHV or non-googly amplitudes are also briefly discussed, in particular the purely fermionic amplitude with 3 quark-antiquark pairs.

An investigation of the 109Cd γ-ray induced K-x-ray fluorescence (XRF) bone-lead measurement calibration procedure

Two sets of phantoms have been used to calibrate a 109Cd γ-ray induced K-XRF bone-lead measurement system. Both sets of phantoms are made of plaster of Paris, but the calibration lines are significantly different. This results in a significant difference for the derived concentrations of bone lead for the same person using these two sets of phantoms. This study shows that the different calibration lines are due to the different compositions of the phantoms, which can then be accounted for by adjusting the parameters related to the phantom composition in spectral analysis. Bone-lead concentrations for ten lead-exposed smelter workers were computed before and after analysis modification, and the results show that the bone-lead concentrations for the same person calculated from two sets of phantoms are not significantly different, only after the modifications are incorporated. Through these investigations, it was discovered that a common practice of setting the ratio of the calcium edge amplitude to the coherent scatter amplitude as a constant is only valid when all spectra are acquired at the same system resolution. When there is a change in the resolution between spectra, it has been determined that the ratio of the calcium edge amplitude to the coherent area should instead be used as the constant factor in the analysis program.

Semi-Classical Behavior of the Scattering Amplitude for Trapping Perturbations at Fixed Energy

AbstractWe study the semi-classical behavior ash→ 0 of the scattering amplitudef(θ, ω, λ,h) associated to a Schrödinger operatorwith short-range trapping perturbations. First we realize a spatial localization in the general case and we deduce a bound of the scattering amplitude on the real line. Under an additional assumption on the resonances, we show that if we modify the potentialV(x) in a domain lying behind the barrier ﹛x:V(x) > λ﹜, the scattering amplitudef(θ, ω, λ,h) changes by a term of order(h∞). Under an escape assumption on the classical trajectories incoming with fixed direction ω, we obtain an asymptotic development off(θ, ω, λ,h) similar to the one established in the non-trapping case.

MHV Vertices and Scattering Amplitudes in Gauge Theory

The generic googly amplitudes in gauge theory are computed by using the Cachazo-Svrcek-Witten approach to perturbative calculation in gauge theory and the results are in agreement with the previously well-known ones. Within this approach we also discuss the parity transformation, charge conjugation and the dual Ward identity. We also extend this calculation to include fermions and the googly amplitudes with a single quark-anti-quark pair are obtained correctly from fermionic MHV vertices. At the end we briefly discuss the possible extension of this approach to gravity.

Glueball Scattering Amplitudes from Holography

Using techniques developed in a previous paper three-point functions in field theories described by holographic renormalization group flows are computed. We consider a system of one active scalar and one inert scalar coupled to gravity. For the GPPZ flow, their dual operators create states that are interpreted as glueballs of the N=1 SYM theory, which lies at the infrared end of the renormalization group flow. The scattering amplitudes for three-glueball processes are calculated providing precise predictions for glueball decays in N=1 SYM theory. Numerical results for low-lying glueballs are included.

Statistics of Fluctuations in High-Frequency Low-Grazing-Angle Backscatter From a Rocky Sea Bed

This paper examines the fluctuations in low-grazing-angle 100-kHz backscatter from a rocky limestone sea bed near Copenhagen, Denmark, at horizontal ranges up to 420 m. The sea-bed reverberation was characterized by strong short spatial-scale variations in scattering strength and statistical parameters. The measured areal backscatter strengths were in the range from -50 to -24 dB at grazing angles less than 3/spl deg/, showing a strong local variability and grazing-angle dependence definitely not in accordance with Lambert's law. The observed echo-amplitude distributions varied between log-normal and Rayleigh models, with more Rayleigh-like probability density functions having higher scintillation indices and skewness (approaching values of 1.0 and 0.63, respectively). The scintillation index and skewness parameters were found to increase mildly with both horizontal range and water-current magnitude. A simple model using the coherent superposition of multiple scatterers was proposed to explain the observed scattering statistics. This model is based on the assumption that the sea bed is effectively immobile, with water-borne scintillation and micro-multipaths providing fluctuations in scatterer phase. This simple model shows that echo-amplitude fluctuations can deviate from the Rayleigh model through two mechanisms: 1) decreasing the levels of water-borne phase fluctuation and 2) increasing the nonuniformity of the sea-bed scatterer amplitudes.

Dispersion Relations for the Forward Elastic Scattering Amplitude in Noncommutative Quantum Field Theory

We show that the forward elastic scattering amplitude of two massive spinless particles in noncommutative quantum field theory has the same analytic properties as in the commutative case if the noncommutativity condition involves only the spatial variables.

Microlocalization of Resonant States and Estimates of the Residue of the Scattering Amplitude

We obtain some microlocal estimates of the resonant states associated to a resonance z 0 of an h-differential operator. More precisely, we show that the normalized resonant states are outside the set of trapped trajectories and are in the incoming area of the phase space. As an application, we show that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector. Finally we prove such a bound in some examples.

Gauge Fixing and Scattering Amplitudes in String Field Theory Expanded around Universal Solutions

We study a gauge fixed action of open string field theory expanded around the universal solution which has been found as an analytic classical solution with one parameter a. For a>-1/2, we are able to reproduce open string scattering amplitudes in the theory fixed in the Siegel gauge. At a=-1/2, all scattering amplitudes vanish and there is no open string excitation in the gauge fixed theory. These results support the conjecture that the universal solution can be regarded as pure gauge or the tachyon vacuum solution.

Magnetic field effects on the optical response of a film with a rough surface: Voigt geometry

Using the Rayleigh–Fano modal approach we investigate the optical response of a metallic film with a deterministic rough surface taking into account an external magnetic field in the Voigt geometry. For P-polarized light incident onto a deterministic rough surface we calculate the specular and first-order scattered field amplitudes. We also explore the nonreciprocity property and the coupling of the incident light with the surface magnetoplasmons. It is obtained that the magnetic field strength may increase the gap between two minima produced by the splitting of the minima of the zero-field specular reflection. The dispersion relations of the surface magnetoplasmons predict the possible experimental excitation and detection of these modes.

Recovery of Small Inhomogeneities from the Scattering Amplitude at a Fixed Frequency

We rigorously derive the leading order term in the asymptotic expansion of the scattering amplitude of a collection of a finite number of dielectric inhomogeneities of small diameter. We then apply this asymptotic formula for the purpose of identifying the location and certain properties of the shapes of the small inhomogeneities from scattering amplitude measurements at a fixed frequency. Our main idea is to reduce this reconstruction problem to the calculation of an inverse Fourier transform.

Gauge Fixing and Scattering amplitudes in String Field Theory around Universal Solutions

Gauge Fixing and Scattering amplitudes in String Field Theory around Universal Solutions

Computation of the Scattering Amplitude of a Wave Diffracted by the Vertex of a Cone of Arbitrary Shape

A method of computing (a version of the Abel―Poisson method of summing divergent series) the scattering amplitude of a wave diffracted by the vertex of a cone of arbitrary shape is justified. With the help of the techniques of parabolic operators, it is shown that the approximation, as well as all the derivatives of it, converges uniformly in the region of regularity of the scattering amplitude. Bibliography: 5 titles.

High-Energy Relations Between Elastic Scattering Amplitudes of Particles and Antiparticles

We find conditions under which the ratio of particle and antiparticle total scattering cross sections →∞ as s→∞. If the forward elastic scattering amplitudes become purely real asymptotically, then their ratio tends to −1. We prove that /σ−(s)≅1 for σ+(s)≫π/mπ2, where mπ is the π-meson mass. We show that the asymptotic relations obtained have finite-energy analogues for some processes.