scholarly journals UNITARITY OF THE AHARONOV–BOHM SCATTERING AMPLITUDES

1998 ◽  
Vol 13 (05) ◽  
pp. 831-840 ◽  
Author(s):  
MASATO ARAI ◽  
HISAKAZU MINAKATA
Keyword(s):  
Scattering Amplitudes ◽  
Plane Wave ◽  
Incident Wave ◽  
Theoretical Foundation ◽  
Scattering Amplitude ◽  
The Other ◽  
Unitarity Relation ◽  
Incident Waves ◽  
Aharonov Bohm

We discuss the unitarity relation of the Aharonov–Bohm scattering amplitude with the hope that it distinguishes between the differing treatment which employ different incident waves. We find that the original Aharonov–Bohm scattering amplitude satisfies the unitarity relation under the regularization prescription whose theoretical foundation does not appear to be understood. On the other land, the amplitude obtained by Ruijsenaars who uses plane wave as incident wave also satisfies the unitarity relation but in an unusual way.

SCATTERING OF A PLANE WAVE FROM A CIRCULAR DIELECTRIC CYLINDER AT OBLIQUE INCIDENCE

1955 ◽  
Vol 33 (5) ◽  
pp. 189-195 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Incident Wave ◽  
Oblique Incidence ◽  
Normal Incidence ◽  
The Other ◽  
Infinite Length ◽  
Dielectric Cylinder ◽  
Magnetic Vector ◽  
Plane Wave Incident

A solution is given for the problem of a plane wave incident obliquely on a circular cylinder of infinite length. The electric properties of the cylinder are taken to be homogeneous and isotropic but otherwise arbitrary. It is shown that in the general case the scattered field contains a significant cross-polarized component which vanishes at normal incidence. While the solution is derived for the magnetic vector of the incident wave transverse to the axis of the cylinder, the corresponding result for the other polarization can be obtained from symmetry.

Resonance tunnelling of waves in a stratified cold plasma

1979 ◽  
Vol 290 (1374) ◽  
pp. 405-433 ◽  
Keyword(s):  
Refractive Index ◽  
Incident Wave ◽  
Cold Plasma ◽  
Oblique Incidence ◽  
Formal Proof ◽  
The Other ◽  
Governing Equations ◽  
Free System ◽  
Transmitted Waves ◽  
Incident Waves

The theory of the tunnelling of waves through a barrier in which the square of the effective refractive index is zero at one boundary and infinite at or near the other is studied. An infinity of the refractive index is called a resonance and so we speak of resonance tunnelling. The sum of the powers in the reflected and transmitted waves is less than the power in the incident wave even in a loss free system where there is no mechanism for the absorption of energy. A formal proof is given that there must be such a disappearance of energy, associated with the solution of the governing equations that is singular at the resonance. The problem of what has happened to the lost energy is discussed. Some previous treatments dealt only with normally incident waves, but this is a degenerate case. The theory is extended to include oblique incidence and some new features are revealed. Some specific examples are worked out as illustrations.

scholarly journals Numerical approximation of the scattering amplitude in elasticity

SeMA Journal ◽  
2021 ◽  
Author(s):  
Juan A. Barceló ◽  
Carlos Castro
Keyword(s):  
Scattering Amplitudes ◽  
Numerical Approximation ◽  
Scattering Amplitude ◽  
Constant Matrix ◽  
Numerical Examples ◽  
Elasticity System ◽  
Matrix Potential ◽  
Scattering Field ◽  
Incident Waves ◽  
Operator Convergence

AbstractWe propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $$d=2$$ d = 2 and 3. This requires to approximate first the scattering field, for some incident waves, which can be written as the solution of a suitable Lippmann-Schwinger equation. In this work we adapt the method introduced by Vainikko (Res Rep A 387:3–18, 1997) to solve such equations when considering the Lamé operator. Convergence is proved for sufficiently smooth potentials. Implementation details and numerical examples are also given.

scholarly journals On the acoustic scattering amplitude for a multi-layered Scatterer

1998 ◽  
Vol 39 (4) ◽  
pp. 431-448 ◽  
Author(s):  
Christodoulos Athanasiadis
Keyword(s):  
Scattering Amplitudes ◽  
General Theory ◽  
Plane Wave ◽  
Boundary Value Problems ◽  
Cross Section ◽  
Scattering Amplitude ◽  
Boundary Value ◽  
Acoustic Scattering ◽  
Scattering Cross ◽  
Time Harmonic

AbstractWe consider the boundary-value problems corresponding to the scattering of a time-harmonic acoustic plane wave by a multi-layered obstacle with a sound-soft, hard or penetrable core. Firstly, we construct in closed forms the normalized scattering amplitudes and prove the classical reciprocity and scattering theorems for these problems. These results are then used to study the spectrum of the scattering amplitude operator. The scattering cross-section is expressed in terms of the forward value of the corresponding normalized scattering amplitude. Finally, we develop a more general theory for scattering relations.

Constructing Prophetic Divination

2017 ◽  
Author(s):  
Martti Nissinen
Keyword(s):  
Comparative Studies ◽  
Theoretical Foundation ◽  
Eastern Mediterranean ◽  
Source Material ◽  
The Other ◽  
Near Eastern ◽  
Common Category ◽  
Divine Knowledge ◽  
Historical Phenomenon

This chapter lays the theoretical foundation of the book, defining prophecy as a non-technical, or inspired, form of divination, in which the prophet acts as an intermediary of divine knowledge. It is argued that prophecy is as much a scholarly construct as a historical phenomenon documented in Near Eastern, biblical, as well as Greek textual sources. The knowledge of the historical phenomenon depends essentially on the genre and purpose of the source material which, however, is very fragmentary and, due to its secondary nature, does not yield a full and balanced picture of ancient prophecy. The chapter also discusses the purpose of comparative studies, arguing that they are necessary, not primarily to reveal the influence of one source on the other, but to identify a common category of ancient Eastern Mediterranean prophecy.

scholarly journals Two-parton scattering amplitudes in the Regge limit to high loop orders

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Simon Caron-Huot ◽  
Einan Gardi ◽  
Joscha Reichel ◽  
Leonardo Vernazza
Keyword(s):  
Scattering Amplitudes ◽  
Scattering Amplitude ◽  
Dimensional Regularization ◽  
High Energy ◽  
Logarithmic Order ◽  
Finite Radius ◽  
High Loop ◽  
Parton Scattering ◽  
Infrared Divergences ◽  
Regge Limit

Abstract We study two-to-two parton scattering amplitudes in the high-energy limit of perturbative QCD by iteratively solving the BFKL equation. This allows us to predict the imaginary part of the amplitude to leading-logarithmic order for arbitrary t-channel colour exchange. The corrections we compute correspond to ladder diagrams with any number of rungs formed between two Reggeized gluons. Our approach exploits a separation of the two-Reggeon wavefunction, performed directly in momentum space, between a soft region and a generic (hard) region. The former component of the wavefunction leads to infrared divergences in the amplitude and is therefore computed in dimensional regularization; the latter is computed directly in two transverse dimensions and is expressed in terms of single-valued harmonic polylogarithms of uniform weight. By combining the two we determine exactly both infrared-divergent and finite contributions to the two-to-two scattering amplitude order-by-order in perturbation theory. We study the result numerically to 13 loops and find that finite corrections to the amplitude have a finite radius of convergence which depends on the colour representation of the t-channel exchange.

Study of wave attenuation in concrete

1993 ◽  
Vol 8 (9) ◽  
pp. 2344-2353 ◽  
Author(s):  
J-M. Berthelot ◽  
Souda M. Ben ◽  
J.L. Robert
Keyword(s):  
Experimental Study ◽  
Plane Wave ◽  
Wave Attenuation ◽  
Plane Waves ◽  
Propagation Distance ◽  
Experimental Results ◽  
The Other ◽  
Wave Frequency ◽  
Concrete Composition ◽  
Analytical Expression

The experimental study of wave attenuation in concrete has been achieved in the case of the propagation of plane waves in concrete rods. Different mortars and concretes have been investigated. A transmitter transducer coupled to one of the ends of the concrete rod generates the propagation of a plane wave in the rod. The receiver transducer, similar to the previous one, is coupled to the other end of the rod. The experimental results lead to an analytical expression for wave attenuation as function of the concrete composition, the propagation distance, and the wave frequency.

scholarly journals Universal opening of four-loop scattering amplitudes to trees

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Selomit Ramírez-Uribe ◽  
Roger J. Hernández-Pinto ◽  
Germán Rodrigo ◽  
German F. R. Sborlini ◽  
William J. Torres Bobadilla
Keyword(s):  
Scattering Amplitudes ◽  
General Expression ◽  
High Energy Physics ◽  
Scattering Amplitude ◽  
Causal Structure ◽  
High Energy ◽  
Quantum Field Theories ◽  
Efficient Computation ◽  
Perturbative Approach ◽  
Theoretical Predictions

Abstract The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these calculations, some ingredients remain specially challenging. This is the case of multiloop scattering amplitudes that constitute a hard bottleneck to solve. In this paper, we delve into the application of a disruptive technique based on the loop-tree duality theorem, which is aimed at an efficient computation of such objects by opening the loops to nondisjoint trees. We study the multiloop topologies that first appear at four loops and assemble them in a clever and general expression, the N4MLT universal topology. This general expression enables to open any scattering amplitude of up to four loops, and also describes a subset of higher order configurations to all orders. These results confirm the conjecture of a factorized opening in terms of simpler known subtopologies, which also determines how the causal structure of the entire loop amplitude is characterized by the causal structure of its subtopologies. In addition, we confirm that the loop-tree duality representation of the N4MLT universal topology is manifestly free of noncausal thresholds, thus pointing towards a remarkably more stable numerical implementation of multiloop scattering amplitudes.

scholarly journals Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Daniel Omondi Onyango ◽  
Robert Kinyua ◽  
Abel Nyakundi Mayaka
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Plane Wave ◽  
Acoustic Pressure ◽  
Three Dimensional ◽  
The Other ◽  
Expansion Chamber ◽  
Central Tube ◽  
Simple Expansion ◽  
Plane Wave Propagation

The shape of the modal duct of an acoustic wave propagating in a muffling system varies with the internal geometry. This shape can be either as a result of plane wave propagation or three-dimensional wave propagation. These shapes depict the distribution of acoustic pressure that may be used in the design or modification of mufflers to create resonance at cut-off frequencies and hence achieve noise attenuation or special effects on the output of the noise. This research compares the shapes of acoustic duct modes of two sets of four pitch configurations of a helicoid in a simple expansion chamber with and without a central tube. Models are generated using Autodesk Inventor modeling software and imported into ANSYS 18.2, where a fluid volume from the complex computer-aided-design (CAD) geometry is extracted for three-dimensional (3D) analysis. Mesh is generated to capture the details of the fluid cavity for frequency range between 0 and 2000Hz. After defining acoustic properties, acoustic boundary conditions and loads were defined at inlet and outlet ports before computation. Postprocessed acoustic results of the modal shapes and transmission loss (TL) characteristics of the two configurations were obtained and compared for geometries of the same helical pitch. It was established that whereas plane wave propagation in a simple expansion chamber (SEC) resulted in a clearly defined acoustic pressure pattern across the propagation path, the distribution in the configurations with and without the central tube depicted three-dimensional acoustic wave propagation characteristics, with patterns scattering or consolidating to regions of either very low or very high acoustic pressure differentials. A difference of about 80 decibels between the highest and lowest acoustic pressure levels was observed for the modal duct of the geometry with four turns and with a central tube. On the other hand, the shape of the TL curve shifts from a sinusoidal-shaped profile with well-defined peaks and valleys in definite multiples of π for the simple expansion chamber, while that of the other two configurations depended on the variation in wavelength that affects the location of occurrence of cut-on or cut-off frequency. The geometry with four turns and a central tube had a maximum value of TL of about 90 decibels at approximately 1900Hz.

Sign in / Sign up

Export Citation Format

Share Document