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.

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.

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.

Diffraction by a half-plane perpendicular to the distinguished axis of a general gyrotropic medium

1977 ◽  
Vol 55 (4) ◽  
pp. 305-324 ◽  
Author(s):  
S. Przeździecki ◽  
R. A. Hurd
Keyword(s):  
Half Plane ◽  
Fourier Transforms ◽  
Diffraction Problem ◽  
Plane Waves ◽  
Closed Form Solution ◽  
Basic Feature ◽  
Form Solution ◽  
Electromagnetic Plane Wave ◽  
Edge Diffraction ◽  
Special Cases

An exact, closed-form solution is found for the following half-plane diffraction problem: (I) The medium surrounding the half-plane is both electrically and magnetically gyrotropic. (II) The scattering half-plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The incident electromagnetic plane wave propagates in a direction normal to the edge of the half-plane.The formulation of the problem leads to a coupled pair of Wiener–Hopf equations. These had previously been thought insoluble by quadratures, but yield to a newly discovered technique : the Wiener–Hopf–Hilbert method. A basic feature of the problem is its two-mode character i.e. plane waves of both modes are necessary for the spectral representation of the solution. The coupling of these modes is purely due to edge diffraction, there being no reflection coupling. The solution obtained is simple in that the Fourier transforms of the field components are just algebraic functions. Properties of the solution are investigated in some special cases.

DIVISIBLE LOAD DISTRIBUTION IN A NETWORK OF PROCESSORS

2008 ◽  
Vol 09 (01n02) ◽  
pp. 31-51 ◽  
Author(s):  
SAMEER BATAINEH
Keyword(s):  
Closed Form ◽  
Load Distribution ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Other ◽  
Optimum Number ◽  
Sequencing Problem ◽  
Divisible Load ◽  
Finish Time ◽  
Optimum Sequence

The paper presents a closed form solution for an optimum scheduling of a divisible job on an optimum number of processor arranged in an optimum sequence in a multilevel tree networks. The solution has been derived for a single divisible job where there is no dependency among subtasks and the root processor can either perform communication and computation at the same time. The solution is carried out through three basic theorems. One of the theorems selects the optimum number of available processors that must participate in executing a divisible job. The other solves the sequencing problem in load distribution by which we are able to find the optimum sequence for load distribution in a generalized form. Having the optimum number of processors and their sequencing for load distribution, we have developed a closed form solution that determines the optimum share of each processor in the sequence such that the finish time is minimized. Any alteration of the number of processors, their sequences, or their shares that are determined by the three theorems will increase the finish time.

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.

Bi-BCM: A Closed-Form Solution for Fixed-Guided Beams in Compliant Mechanisms

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Fulei Ma ◽  
Guimin Chen
Keyword(s):  
Closed Form ◽  
Compliant Mechanisms ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Other ◽  
Boundary Line ◽  
Final Solution ◽  
Second Mode ◽  
Design Calculations ◽  
Constraint Model

A fixed-guided beam, with one end is fixed while the other is guided in that the angle of that end does not change, is one of the most commonly used flexible segments in compliant mechanisms such as bistable mechanisms, compliant parallelogram mechanisms, compound compliant parallelogram mechanisms, and thermomechanical in-plane microactuators. In this paper, we split a fixed-guided beam into two elements, formulate each element using the beam constraint model (BCM) equations, and then assemble the two elements' equations to obtain the final solution for the load–deflection relations. Interestingly, the resulting load–deflection solution (referred to as Bi-BCM) is closed-form, in which the tip loads are expressed as functions of the tip deflections. The maximum allowable axial force of Bi-BCM is the quadruple of that of BCM. Bi-BCM also extends the capability of BCM for predicting the second mode bending of fixed-guided beams. Besides, the boundary line between the first and the second modes bending of fixed-guided beams can be easily obtained using a closed-form equation. Bi-BCM can be immediately used for quick design calculations of compliant mechanisms utilizing fixed-guided beams as their flexible segments (generally no iteration is required). Different examples are analyzed to illustrate the usage of Bi-BCM, and the results show the effectiveness of the closed-form solution.

Spontaneous potential log response expressed as convolution

Geophysics ◽  
1982 ◽  
Vol 47 (9) ◽  
pp. 1335-1337
Author(s):  
E. A. Nosal
Keyword(s):  
Closed Form ◽  
Signal Analysis ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Other ◽  
Individual Contribution ◽  
Spontaneous Potential ◽  
The Earth ◽  
The Individual ◽  
Special Case

A special case of spontaneous potential (SP) logging, which has a closed‐form solution, will be expressed as a convolutional operation. Such a formal demonstration serves two purposes. First, it separates the individual contribution of the tool from that of the earth. Second, it places this logging device within the mathematical context of signal analysis. The special case for which a closed‐form solution is known is that where all resistivities are equal. Fourier analysis applied to this solution leads to a product of two functions, of which one is identified as the contribution of the earth and the other of the tool.

An Inverse Force Analysis of a Tetrahedral Three-Spring System

1995 ◽  
Vol 117 (2A) ◽  
pp. 286-291 ◽  
Author(s):  
P. Dietmaier
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Other ◽  
Force Analysis ◽  
Equilibrium Configurations ◽  
Spring System ◽  
The Common ◽  
The Stability ◽  
Inverse Force

A tetrahedral three-spring system under a single load has been analyzed and a closed-form solution for the equilibrium positions is given. Each of the three springs is attached at one end to a fixed pivot in space while the other three ends are linked by a common pivot. The springs are assumed to behave in a linearly elastic way. The aim of the paper at hand was to find out what the maximum number of equilibrium positions of such a system might be, and how to compute all possible equilibrium configurations if a given force is applied to the common pivot. First a symmetric and unloaded system was studied. For such a system it was shown that there may exist a maximum of 22 equilibrium configurations which may all be real. Second the general, loaded system was analyzed, revealing again a maximum of 22 real equilibrium configurations. Finally, the stability of this three-spring system was investigated. A numerical example illustrates the theoretical findings.

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