scholarly journals On hearing the shape of an arbitrary doubly-connected region in R2

1990 ◽  
Vol 31 (4) ◽  
pp. 472-483 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Asymptotic Expansion ◽  
Spectral Function ◽  
Basic Problem ◽  
Outer Boundary ◽  
Connected Region ◽  
Two Dimensional ◽  
Complete Knowledge ◽  
Impedance Condition

AbstractThe basic problem in this paper is that of determining the geometry of an arbitrary doubly-connected region in R2 together with an impedance condition on its inner boundary and another impedance condition on its outer boundary, from the complete knowledge of the eigenvalues for the two-dimensional Laplacian using the asymptotic expansion of the spectral function for small positive t.

scholarly journals Hearing the shape of an annular drum

1983 ◽  
Vol 24 (4) ◽  
pp. 435-438 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Asymptotic Expansion ◽  
Spectral Function ◽  
Bessel Functions ◽  
Direct Calculation ◽  
Eigenvalue Equation ◽  
Connected Region ◽  
Laplacian Operator ◽  
Geometrical Properties ◽  
Annular Membrane

AbstractThe asymptotic expansion for a spectral function of the Laplacian operator, involving geometrical properties of the domain, is demonstrated by direct calculation for the case of a doubly-connected region in the form of a narrow annular membrane. By utilizing a known formula for the zeros of the eigenvalue equation containing Bessel functions, the area, total perimeter and connectivity are all extracted explicitly.

scholarly journals An inverse eigenvalue problem for an arbitrary multiply connected bounded region inR2

1991 ◽  
Vol 14 (3) ◽  
pp. 571-579 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Asymptotic Expansion ◽  
Basic Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Inverse Eigenvalue Problem ◽  
Bounded Region ◽  
Multiply Connected ◽  
Complete Knowledge ◽  
Inverse Eigenvalue ◽  
The Laplace Operator

The basic problem is to determine the geometry of an arbitrary multiply connected bounded region inR2together with the mixed boundary conditions, from the complete knowledge of the eigenvalues{λi}j=1∞for the Laplace operator, using the asymptotic expansion of the spectral functionθ(t)=∑j=1∞exp(−tλi)ast→0.

SO(5) SYMMETRY AND SINGLE PARTICLE SPECTRA

1999 ◽  
Vol 13 (24n25) ◽  
pp. 3039-3047
Author(s):  
M. G. ZACHER ◽  
A. DORNEICH ◽  
R. EDER ◽  
W. HANKE ◽  
S. C. ZHANG
Keyword(s):  
Spectral Function ◽  
Single Particle ◽  
Photoemission Spectrum ◽  
Two Dimensional ◽  
Ladder Model ◽  
Particle Spectra ◽  
Key Features

We discuss properties of a recently proposed SO(5) symmetric ladder model. Key features of the single particle spectral function that are emerging from the symmetry are numerically identified in the ladder model and in the photoemission spectrum of the two-dimensional t–J model.

scholarly journals To the Solution of Geometric Inverse Heat Conduction Problems

2021 ◽  
Vol 24 (1) ◽  
pp. 6-12
Author(s):  
Yurii M. Matsevytyi ◽  
◽  
Valerii V. Hanchyn ◽  
Keyword(s):  
Heat Conduction ◽  
Iterative Process ◽  
Regularization Parameter ◽  
Outer Boundary ◽  
Linear Equations ◽  
The Body ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
System Of Linear Equations ◽  
Inverse Heat Conduction Problems

On the basis of A. N. Tikhonov’s regularization theory, a method is developed for solving inverse heat conduction problems of identifying a smooth outer boundary of a two-dimensional region with a known boundary condition. For this, the smooth boundary to be identified is approximated by Schoenberg’s cubic splines, as a result of which its identification is reduced to determining the unknown approximation coefficients. With known boundary and initial conditions, the body temperature will depend only on these coefficients. With the temperature expressed using the Taylor formula for two series terms and substituted into the Tikhonov functional, the problem of determining the increments of the coefficients can be reduced to solving a system of linear equations with respect to these increments. Having chosen a certain regularization parameter and a certain function describing the shape of the outer boundary as an initial approximation, one can implement an iterative process. In this process, the vector of unknown coefficients for the current iteration will be equal to the sum of the vector of coefficients in the previous iteration and the vector of the increments of these coefficients, obtained as a result of solving a system of linear equations. Having obtained a vector of coefficients as a result of a converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to select the regularization parameter in such a way that this discrepancy is within the measurement error. The method itself and the ways of its implementation are the novelty of the material presented in this paper in comparison with other authors’ approaches to the solution of geometric inverse heat conduction problems. When checking the effectiveness of using the method proposed, a number of two-dimensional test problems for bodies with a known location of the outer boundary were solved. An analysis of the influence of random measurement errors on the error in identifying the outer boundary shape is carried out.

scholarly journals Spectral function of two-dimensional Fermi liquids

1998 ◽  
Vol 57 (15) ◽  
pp. 8873-8877 ◽  
Author(s):  
Christoph J. Halboth ◽  
Walter Metzner
Keyword(s):  
Spectral Function ◽  
Fermi Liquids ◽  
Two Dimensional

scholarly journals A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Fushan Li
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Laplace Transformation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Nonlinear Viscoelastic ◽  
Leading Term ◽  
Viscoelastic Shells

By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional nonlinear viscoelastic shells model satisfied by the leading term of asymptotic expansion of the solution to the three-dimensional equations.

Free Convection in a Two-Dimensional Porous Loop

1986 ◽  
Vol 108 (2) ◽  
pp. 277-283 ◽  
Author(s):  
L. Robillard ◽  
T. H. Nguyen ◽  
P. Vasseur
Keyword(s):  
Steady State ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Outer Boundary ◽  
Convective Motion ◽  
Steady State Solution ◽  
Temperature Fields ◽  
Maximum Temperature ◽  
Two Dimensional ◽  
Convective Cells

A study is made of the natural convection in an annular porous layer having an isothermal inner boundary and its outer boundary subjected to a thermal stratification arbitrarily oriented with respect to gravity. For such conditions, no symmetry can be expected for the flow and temperature fields with respect to the vertical diameter and the whole circular region must be considered. Two-dimensional steady-state solutions are sought by perturbation and numerical approaches. Results obtained indicate that the circulating flow around the annulus attains its maximum strength when the stratification is horizontal (heating from the side). This circulating flow is responsible for an important heat exchange between the porous layer and its external surroundings. The flow field is also characterized by the presence of two convective cells near the inner boundary, giving rise to flow reversal on this surface. When the maximum temperature on the outer boundary is at the bottom of the cavity, the convective motion becomes potentially unstable; for a Rayleigh number below 80, there exists a steady-state solution symmetrical with respect to both vertical and horizontal axes; for a Rayleigh number above 80, an unsteady periodic situation develops with the circulating flow alternating its direction around the annulus.

Irrotational flow past bodies close to a plane surface

1971 ◽  
Vol 50 (3) ◽  
pp. 481-491 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Asymptotic Expansion ◽  
Numerical Computation ◽  
Potential Flow ◽  
Close Agreement ◽  
Plane Surface ◽  
Three Dimensional ◽  
Ground Surface ◽  
Two Dimensional ◽  
General Shape ◽  
Irrotational Flow

A theroetical analysis is given for potential flow over, around and under a vehicle of general shape moving close to a plane ground surface. Solutions are given both in the form of a small-gap asymptotic expansion and a direct numerical computation, with close agreement between the two for two-dimensional flows with and without circulation. Some results for three-dimensional bodies are discussed.

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