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 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.

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.

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 Numerical Approximation of the Space Fractional Cahn-Hilliard Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Zhifeng Weng ◽  
Langyang Huang ◽  
Rong Wu
Keyword(s):  
Numerical Approximation ◽  
Second Order ◽  
Differentiation Formula ◽  
Numerical Examples ◽  
Backward Differentiation Formula ◽  
Hilliard Equation ◽  
Order Case ◽  
Energy Stable ◽  
Cahn Hilliard Equation ◽  
Fourier Spectral Methods

In this paper, a second-order accurate (in time) energy stable Fourier spectral scheme for the fractional-in-space Cahn-Hilliard (CH) equation is considered. The time is discretized by the implicit backward differentiation formula (BDF), along with a linear stabilized term which represents a second-order Douglas-Dupont-type regularization. The semidiscrete schemes are shown to be energy stable and to be mass conservative. Then we further use Fourier-spectral methods to discretize the space. Some numerical examples are included to testify the effectiveness of our proposed method. In addition, it shows that the fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case.

scholarly journals A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 89 ◽  
Author(s):  
Manuel Echeverry ◽  
Carlos Mejía
Keyword(s):  
Inverse Problem ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Two Dimensional ◽  
Regularization Procedure ◽  
Numerical Examples ◽  
Convergence Results ◽  
Time Fractional Diffusion Equation ◽  
Operator Convergence

We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional discrete mollification operator. Convergence results and illustrative numerical examples are included.

scholarly journals The scattering of slow neutrons by ortho - and para -hydrogen

1955 ◽  
Vol 230 (1180) ◽  
pp. 19-32 ◽  
Keyword(s):  
Scattering Amplitudes ◽  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Coherent Scattering ◽  
Para Hydrogen ◽  
Cavendish Laboratory ◽  
Proton Interaction ◽  
Scattering Cross Sections ◽  
Slow Neutrons

The neutron velocity selector of the Cavendish Laboratory has been used to measure the scattering cross-sections of ortho- and para -hydrogen for slow neutrons. The triplet and singlet scattering amplitudes of the neutron-proton interaction may be deduced from these cross-sections. The values obtained are a t = (0·537 ± 0·004) x 10 -12 cm, a s = -(2·373 ±0·007) x 10 -12 cm, where a t and a s are the triplet and singlet scattering amplitudes respectively. The values of the coherent scattering amplitude ƒ = 2(3/4 a +1/4 a ), and of the free proton cross-section σ ƒ = 4π(3/4 a 2 t + 1/4 a 2 s given by the above values of a t and a s , are ƒ = -(0·380 ± 0·005) x 10 -12 cm, σ ƒ = (20·41 ± 0·14) x 10 -24 cm 2 .

scholarly journals Messung der kohärenten Streuamplitude für die Neutron-Deuteron- Wechselwirkung am Neutronenschwerkraftrefraktometer des FRM / Measurement of the n-d Coherent Scattering Amplitude Using the Neutron Gravity Refractometer at the Research Reactor of the Technical University of Munich

1974 ◽  
Vol 29 (9) ◽  
pp. 1284-1290 ◽  
Author(s):  
Wolfgang Nistler
Keyword(s):  
Scattering Amplitudes ◽  
Research Reactor ◽  
Scattering Amplitude ◽  
Coherent Scattering ◽  
Mirror Reflection ◽  
Light Water ◽  
University Of Munich ◽  
Technical University ◽  
Deuterium Nucleus

Measurements of the coherent scattering amplitudes of various mixtures of heavy and light water are reported. By means of mirror reflection technique the coherent scattering amplitudes of the D2O and H2O molecule are determined to be 19.148±0.004 F and -1.679±0.004 F, respectively. Use of aH=-3.740±0.003 F, obtained by the same technique, yields aD=6.674±0.006 F as the bound scattering amplitude of the deuterium nucleus. This value disagrees with the widely accepted 6.21±0.04 F, reported by Bartolini et al. in 1968.

Inverse scattering problem and the Schwinger approximation

1992 ◽  
Vol 70 (4) ◽  
pp. 282-288 ◽  
Author(s):  
M. A. Hooshyar ◽  
T. H. Lam ◽  
M. Razavy
Keyword(s):  
Scattering Amplitudes ◽  
Wave Scattering ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Nucleon Nucleon ◽  
S Wave ◽  
Physical Systems ◽  
Nucleus Scattering ◽  
The Stability

A new method of inversion of the S-wave scattering amplitude based on the Schwinger variational method is presented. This method is accurate and stable and is applicable to a number of interesting physical systems such as nucleon–nucleon or nucleon–nucleus scattering even when the data are known for a finite nonrelativistic range of energies. ⁁Examples of different scattering amplitudes and their corresponding potential functions are given to show the accuracy and the stability of the method.

scholarly journals Numerical approximation of coupled 1D and 2D non-linear Burgers’ equations by employing Modified Quartic Hyperbolic B-spline Differential Quadrature Method

2021 ◽  
Vol 15 ◽  
pp. 37-55
Author(s):  
Mamta Kapoor ◽  
Varun Joshi
Keyword(s):  
Present Method ◽  
Numerical Approximation ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Differential Quadrature Method ◽  
Quadrature Method ◽  
B Spline ◽  
Numerical Examples ◽  
Burgers Equations ◽  
Weighting Coefficients

In this paper, the numerical solution of coupled 1D and coupled 2D Burgers' equation is provided with the appropriate initial and boundary conditions, by implementing "modified quartic Hyperbolic B-spline DQM". In present method, the required weighting coefficients are computed using modified quartic Hyperbolic B-spline as a basis function. These coupled 1D and coupled 2D Burgers' equations got transformed into the set of ordinary differential equations, tackled by SSPRK43 scheme. Efficiency of the scheme and exactness of the obtained numerical solutions is declared with the aid of 8 numerical examples. Numerical results obtained by modified quartic Hyperbolic B-spline are efficient and it is easy to implement

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