Diffraction by an anisotropic impedance half plane

1985 ◽  
Vol 63 (9) ◽  
pp. 1135-1140 ◽  
Author(s):  
R. A. Hurd ◽  
E. Lüneburg
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Half Plane ◽  
Matrix Factorization ◽  
Closed Form Solution ◽  
Form Solution ◽  
Obliquely Incident

We solve a new canonical problem: that of a plane wave obliquely incident on an anisotropic imperfectly conducting half plane. An exact closed-form solution is obtained by factorizing a 2 × 2 Wiener–Hopf matrix. The problem had earlier been considered insoluble, but yields to a combination of new and old matrix-factorization techniques.

Scattering by hard and soft parallel half-planes

1981 ◽  
Vol 59 (12) ◽  
pp. 1879-1885 ◽  
Author(s):  
R. A. Hurd ◽  
E. Lüneburg
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Half Plane ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Normal Derivative ◽  
Form Solution ◽  
The Other ◽  
Total Field

We consider the diffraction of a scalar plane wave by two parallel half-planes. On one half-plane the total field vanishes whilst on the other its normal derivative is zero. This is a new canonical diffraction problem and we give an exact closed-form solution to it. The problem has applications to the design of acoustic barriers.

On the response of steered vertical line arrays to anisotropic noise

1979 ◽  
Vol 367 (1731) ◽  
pp. 539-547
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Approximate Method ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vertical Line ◽  
Acoustic Sensors ◽  
Gain Function ◽  
Line Array ◽  
Arbitrary Anisotropy

An approximate method is presented for evaluating, through the noise gain function, the response of a steered vertical line array of acoustic sensors to anisotrophic, plane-wave noise fields. On the basis of the high- N approximation a closed form solution is obtained for the noise gain function, even for the general case of arbitrary anisotropy. The main features on the noise gain curves are discussed and interpreted in terms of conventional beamforming concepts.

Diffraction by an infinite set of hard and soft parallel half planes

1982 ◽  
Vol 60 (1) ◽  
pp. 1-9 ◽  
Author(s):  
E. Lüneburg ◽  
R. A. Hurd
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Normal Derivative ◽  
Form Solution ◽  
Total Field ◽  
Bifurcation Problems ◽  
Infinite Set

We consider the diffraction of a plane wave by an infinite set of parallel half planes. On alternate half planes the total field or its normal derivative vanishes. An exact closed-form solution to this new canonical diffraction problem is presented. The problem also contains the solution to ten intrinsically different waveguide "bifurcation" problems.

Diffraction by an infinite set of soft/hard parallel half-planes: the Riemann approach

1982 ◽  
Vol 60 (8) ◽  
pp. 1125-1138 ◽  
Author(s):  
E. Lüneburg
Keyword(s):  
Plane Wave ◽  
Boundary Value Problem ◽  
Closed Form ◽  
Closed Form Solution ◽  
Normal Derivative ◽  
Form Solution ◽  
The Other ◽  
Bragg Angle ◽  
Total Field ◽  
Infinite Set

We consider the diffraction of a plane wave by an infinite set of parallel equidistant half-planes. On each plate the total field vanishes on one side and the normal derivative vanishes on the other side. A closed-form solution for Bragg angle incidence is obtained by reducing the boundary value problem to a solvable Riemann problem.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

Sign in / Sign up

Export Citation Format

Share Document