Analytic solutions to the acoustic source reconstruction problem

2008 ◽  
Vol 464 (2095) ◽  
pp. 1697-1718 ◽  
Author(s):  
Cedric Maury ◽  
Teresa Bravo
Keyword(s):  
Degrees Of Freedom ◽  
Stable Solution ◽  
Analytic Solutions ◽  
Energy Concentration ◽  
Unknown Boundary ◽  
Source Reconstruction ◽  
Reconstruction Problem ◽  
Angular Aperture ◽  
Spheroidal Wave Functions ◽  
Boundary Velocity

In this paper, we generalize the recently developed analytical solutions of the radiation modes problem to the determination of closed-form expressions for the singular value expansion of a number of integral operators that map the boundary velocity of a baffled planar structure onto the acoustic pressure radiated in far-field or intermediate regions. Exact solutions to this problem involve prolate spheroidal wave functions that correspond to a set of independent distributions with finite spatial support and maximal energy concentration in a given bandwidth of the transform domain. A stable solution to the inverse source reconstruction problem is obtained by decomposing the unknown boundary velocity into a number of efficiently radiating singular velocity patterns that correspond to the number of degrees of freedom of the radiated field. It is found that the degree of ill-posedness of the inverse problem is significantly reduced, when considering a hemi-circular observation arc with respect to a linear array of sensors, by a factor scaling on the small angular aperture subtended by the observation line. Estimates are derived from the spatial resolution limits that can be achieved in the source reconstruction problem from the dimension of the efficiently radiating subspace.

Analytic solutions of the radiation modes problem and the active control of sound power

2005 ◽  
Vol 461 (2053) ◽  
pp. 55-78 ◽  
Author(s):  
Cedric Maury ◽  
Stephen J. Elliott
Keyword(s):  
Active Control ◽  
Acoustic Radiation ◽  
Special Functions ◽  
Spectral Estimation ◽  
Analytic Solutions ◽  
Energy Concentration ◽  
Spheroidal Wave Functions ◽  
Prolate Spheroidal Wave Functions ◽  
Concentration Problem ◽  
Band Limited

This paper explores the common mathematical foundation of two different problems: the first one arises in electrical engineering for the detection and the spectral estimation of signals in noise and the second one appears in acoustics for the calculation of the acoustic radiation modes of rectangular structures. Although apparently unrelated, it is found that both applications draw on the so–called concentration problem: of determining which functions that are band–limited in one domain have maximal energy concentration within a region of the transform domain. The analytic solutions to problems of this form are seen to involve prolate spheroidal wave functions. In particular, exact expressions are given for the radiation efficiencies and shapes of the radiation modes of a baffled beam as well as their asymptotics. It is shown that a generalization of the concentration problem to the two–dimensional case provides analytic solutions that solve with a good accuracy, although approximately, the radiation problem. The properties of these special functions provide a rigorous basis of understanding some previously observed features of these applications, namely the grouping property of the radiation modes of a baffled panel and the physical limitations for the active control of sound from a panel.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

scholarly journals Inverse Source on Conformal Conic Geometries

2020 ◽  
Author(s):  
Giovanni Leone ◽  
Fortuna Munno ◽  
Rocco Pierri
Keyword(s):  
Inverse Problem ◽  
Radiation Pattern ◽  
Degrees Of Freedom ◽  
Synthesis Problem ◽  
Source Reconstruction ◽  
Conformal Antennas ◽  
Stable Solutions

This manuscript has been accepted for publication on IEEE Transactions on Antennas and Propagation.<br><br><div>Abstract:</div><div>The paper adopts an inverse problem approach to examine the role of some 2D geometries in the source reconstruction from far zone data. It aims at evaluating the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), of the source and pointing out the set of far zone fields corresponding to stable solutions of the inverse problem. Some of the results are relevant to the synthesis problem of conformal antennas, since a general comparison of different source geometries in providing radiation pattern specifications is proposed.</div>

scholarly journals A Translational Three-Degrees-of-Freedom Parallel Mechanism With Partial Motion Decoupling and Analytic Direct Kinematics

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Huiping Shen ◽  
Damien Chablat ◽  
Boxiong Zeng ◽  
Ju Li ◽  
Guanglei Wu ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Design Theory ◽  
Degrees Of Freedom ◽  
Analytic Solutions ◽  
Inverse Kinematic ◽  
Kinematic Modeling ◽  
Topological Design ◽  
Prismatic Joints ◽  
Topological Characteristics ◽  
Three Degrees Of Freedom

Abstract According to the topological design theory and the method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, this paper studied a three-degrees-of-freedom (3-DOF) translational PM that has three advantages, i.e., (i) it consists of three fixed actuated prismatic joints, (ii) the PM has analytic solutions to the direct and inverse kinematic problems, and (iii) the PM is of partial motion decoupling property. First, the main topological characteristics, such as the POC, degree-of-freedom, and coupling degree, were calculated for kinematic modeling. Thanks to these properties, the direct and inverse kinematic problems can be readily solved. Further, the conditions of the singular configurations of the PM were analyzed, which corresponds to its partial motion decoupling property.

scholarly journals Inverse Source on Conformal Conic Geometries

2020 ◽  
Author(s):  
Giovanni Leone ◽  
Fortuna Munno ◽  
Rocco Pierri
Keyword(s):  
Inverse Problem ◽  
Radiation Pattern ◽  
Degrees Of Freedom ◽  
Synthesis Problem ◽  
Source Reconstruction ◽  
Conformal Antennas ◽  
Stable Solutions

This manuscript has been accepted for publication on IEEE Transactions on Antennas and Propagation.<br><br><div>Abstract:</div><div>The paper adopts an inverse problem approach to examine the role of some 2D geometries in the source reconstruction from far zone data. It aims at evaluating the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), of the source and pointing out the set of far zone fields corresponding to stable solutions of the inverse problem. Some of the results are relevant to the synthesis problem of conformal antennas, since a general comparison of different source geometries in providing radiation pattern specifications is proposed.</div>

scholarly journals An empirical Bayesian solution to the source reconstruction problem in EEG

NeuroImage ◽  
2005 ◽  
Vol 24 (4) ◽  
pp. 997-1011 ◽  
Author(s):  
Christophe Phillips ◽  
Jeremie Mattout ◽  
Michael D. Rugg ◽  
Pierre Maquet ◽  
Karl J. Friston
Keyword(s):  
Source Reconstruction ◽  
Reconstruction Problem ◽  
Empirical Bayesian

scholarly journals Inverse Source on Conformal Conic Geometries

2020 ◽  
Author(s):  
Giovanni Leone ◽  
Fortuna Munno ◽  
Rocco Pierri
Keyword(s):  
Inverse Problem ◽  
Radiation Pattern ◽  
Degrees Of Freedom ◽  
Synthesis Problem ◽  
Source Reconstruction ◽  
Conformal Antennas ◽  
Stable Solutions

The paper adopts an inverse problem approach to examine the role of some 2D geometries in the source reconstruction from far zone data. It aims at evaluating the number of independent pieces of information, i.e. the number of degrees of freedom (NDF), of the source and pointing out the set of far zone fields corresponding to stable solutions of the inverse problem. Some of the results are relevant to the synthesis problem of conformal antennas, since a general comparison of different source geometries in providing radiation pattern specifications is proposed.

scholarly journals Analyzing the Stability for the Motion of an Unstretched Double Pendulum Near Resonance

2021 ◽  
Vol 11 (20) ◽  
pp. 9520
Author(s):  
Tarek S. Amer ◽  
Roman Starosta ◽  
Adelkarim S. Elameer ◽  
Mohamed A. Bek
Keyword(s):  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Double Pendulum ◽  
Nonlinear Dynamical ◽  
Near Resonance ◽  
Wide Range ◽  
The Stability ◽  
The Impact

This work looks at the nonlinear dynamical motion of an unstretched two degrees of freedom double pendulum in which its pivot point follows an elliptic route with steady angular velocity. These pendulums have different lengths and are attached with different masses. Lagrange’s equations are employed to derive the governing kinematic system of motion. The multiple scales technique is utilized to find the desired approximate solutions up to the third order of approximation. Resonance cases have been classified, and modulation equations are formulated. Solvability requirements for the steady-state solutions are specified. The obtained solutions and resonance curves are represented graphically. The nonlinear stability approach is used to check the impact of the various parameters on the dynamical motion. The comparison between the attained analytic solutions and the numerical ones reveals a high degree of consistency between them and reflects an excellent accuracy of the used approach. The importance of the mentioned model points to its applications in a wide range of fields such as ships motion, swaying buildings, transportation devices and rotor dynamics.

scholarly journals Evaluation of the Influence of Uncertain Forward Models on the EEG Source Reconstruction Problem

NeuroImage ◽  
2009 ◽  
Vol 47 ◽  
pp. S52
Author(s):  
C. Stahlhut ◽  
M. Mørup ◽  
O. Winther ◽  
L.K. Hansen
Keyword(s):  
Source Reconstruction ◽  
Reconstruction Problem ◽  
Forward Models

scholarly journals Time-Limited Codewords over Band-Limited Channels: Data Rates and the Dimension of the W-T Space

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 924
Author(s):  
Youssef Jaffal ◽  
Ibrahim Abou-Faycal
Keyword(s):  
Degrees Of Freedom ◽  
Additive White Gaussian Noise ◽  
Wave Functions ◽  
Upper And Lower Bounds ◽  
Prolate Spheroidal ◽  
Spheroidal Wave Functions ◽  
Prolate Spheroidal Wave Functions ◽  
Data Rates ◽  
Band Limited ◽  
Discrete Formulation

We consider a communication system whereby T-seconds time-limited codewords are transmitted over a W-Hz band-limited additive white Gaussian noise channel. In the asymptotic regime as WT→∞, it is known that the maximal achievable rates with such a scheme converge to Shannon’s capacity with the presence of 2WT degrees of freedom. In this work we study the degrees of freedom and the achievable information rates for finite values of WT. We use prolate spheroidal wave functions to obtain an information lossless equivalent discrete formulation and then we apply Polyanskiy’s results on coding in the finite block-length regime. We derive upper and lower bounds on the achievable rates and the corresponding degrees of freedom and we numerically evaluate them for sample values of 2WT. The bounds are asymptotically tight and numerical computations show the gap between them decreases as 2WT increases. Additionally, the possible decrease from 2WT in the available degrees of freedom is upper-bounded by a logarithmic function of 2WT.

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