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Bieträge zur potentialtheorie .Hölder, Otto, January 1882 (has links)
Inaug-diss.--Tübingen.
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The electric potential in the neighbourhood of a thin slitAllard, Jean-Louis January 1961 (has links)
When a slit opening is made in a plane electrode forming the boundary between two unequal electric fields, a distortion of the fields occurs. This paper studies the influence of the slit opening on the electrical potential distribution on both sides of the slit.
A theory is developed for calculating the potential at any point, and from it two methods are derived for finding curves of equal potential disturbance. Several computed curves are presented for each method. The curves suggest a simple graphical construction for approximating the potential disturbance at points not too near the slit.
Because the potential disturbance is the same at image points on either side of the slit, it is found that all the important formulas can be expressed in terms of distances, without regard to sign.
To facilitate the reproduction or extension of this work, a computer program in the widely used Fortran language is given for the simpler of the two methods. / Science, Faculty of / Physics and Astronomy, Department of / Graduate
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Calculation of matrix elements for diatomic moleculesBuckmaster, Harvey Allen January 1952 (has links)
A number of potentials have been suggested as approximations to the 'true' potential function for the nuclei of a diatomic molecule. The relative merits of these potentials are discussed. Whenever possible the eigenfunctions and eigenvalues corresponding to these potentials are given. For the Morse potential the calculations of the eigenfunctions and eigenvalues are reproduced in detail. These eigenfunctions are used to derive general formulae for the radial parts of the dipole and quadrupole matrix elements. The expression for the dipole matrix element is
[formula omitted]
and for the quadrupole matrix element
[formula omitted]
The symbols are defined in sections 20, 21, and 22, The expression for M[subscript D] is in agreement with the one derived by Infeld and Hull while the expression for M[subscript Q] is a result which, so far as the author is aware, has not been published in the literature. / Science, Faculty of / Physics and Astronomy, Department of / Graduate
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On Green's function for the Laplace operator in an unbounded domain.Hewgill, Denton Elwood January 1966 (has links)
This thesis Investigates the Green's functions for the operator T defined by
[ Equation omitted ]
Here H ¹₀ (E) is a standard Sobolev space, Δ is the Laplacian, and E is a domain in which is taken to be "quasi-bounded".
In particular we assume that E lies in the half-space x₁ > 0 and is bounded by the surface obtained by rotating φ(x₁) about the x₁-axis, where φ is continuous, φ(x₁) > 0 and φᵏ∈ L₁(0,+∞) for some k > 0.
The Green's function G(x,y,λ) for the operator T + λ is obtained as the limit of the Green's functions for the well known problem on the truncated domain Eₓ=E ∩ [X₁ < X]. Most of the expected properties of the function are developed including the iii equality
[ Equation omitted ]
where K is the fundamental singularity for the domain.
The eigenvalues and eigenfunctions are constructed, and it is shown that
[ Equation omitted ]
where λₓ,n and λn are the eigenvalues for the problem on Eₓ and E respectively. Furthermore, it is shown that the eigenvalues {λn} are positive with no finite limit point, and the corresponding eigenfurictions are complete.
A detailed calculation involving the inequality displayed above shows that some iterate (Gᵏ ̊) of G(x,y,λ) is a Hilbert-Schmidt kernel. From this property of Gᵏ ̊ it follows that the series ∑λn ˉ²ᵏ ̊ is convergent. From the convergence of this series three results are derived. The first one is an expansion formula in terms of the complete set of eigenfunctions, and the second is that some iterate of the Green's function tends to zero on the boundary. The last one Is the construction of the solution H(x,λ,f), for the boundary value problem
ΔH + λH = f
[ Equation omitted ]
for a sufficiently regular f on E.
The final property of the Green's function, namely, that G(x,y,λ) tends to zero on the boundary, is proved using the fact that Gᵏ ̊is zero on the boundary, and certain inequaiitites estimating the iterates G(x,y, λ) is also shown to be unique.
The asymptotic formula [ Equation omitted ]
a generalization of the usual asymptotic formula of Weyl for the eigenvalues, first given by C. Clark, is derived for these quasi-bounded domains. Finally, the usual asymptotic formula due to Carleman for the eigenfunctions is shown to remain valid. / Science, Faculty of / Mathematics, Department of / Graduate
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Nonlocal potentials and the generalized Levinson's theorem /Qadri, Syed B. January 1979 (has links)
No description available.
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Nonlocal potentials and nuclear resonance scattering /Iwasaki, Masayuki January 1985 (has links)
No description available.
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Error bounds in discrete potential theory /Mathis, Robert Fletcher January 1969 (has links)
No description available.
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Annular functions in potential theory and probability /Howell, Russell William January 1974 (has links)
No description available.
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On the numerical interpretation of gravity and other potential field anomalies caused by layers of varying thicknessAdotevi-Akue, George Modesto 29 April 1971 (has links)
This thesis involves the interpretation of gravity and other
potential field anomalies caused by layers of varying thickness. The
partial differential equations of potential field theory are reviewed for
gravitational and magnetic force fields. A similar review is carried
out for steady-state heat transport and diffusion processes. For the
gravitational force fields, solutions of the partial differential equations
are listed in integral form for the following cases: single body with given
constant density, infinitely thin sheet with variable mass density, two
homogeneous layers with a slowly undulating interface and two layers
with a vertically-constant-density lower layer. The solutions give the
gravity anomaly in terms of the parameters of the source body. Heat
transport phenomena of a similar nature are also discussed.
The general expression obtained for the two homogeneous layers
with a slowly undulating interface is used as an integral equation and
applied to the derivation of crustal thickness variation in Oregon on
the basis of two different computational methods. The first method,
called the digitized algebraic method, solves the quasi-linearized
form of the general integral equation by an iterative technique for three
reference va1ues of the mean depth of the crust-mantle interface, viz.,
25 km, 30 km, and 35 km. The second approach, called the second
derivative approximation method, gives a solution by the Fourier
transform technique to the linearized form of the general integral
equation for the same three reference values of the mean depth of the
crust-mantle interface.
The above results as to the depth of the crust-mantle interface
are compared with recent results with seismic refraction and dispersion data obtained along a profile in eastern Oregon. The value of
the reference depth d which best reconciles with the above results
and the seismic results turns out to be 30.25 km for the depth data on
the basis of the algebraic method and 28.90 km for the depth data
obtained with the second derivative approximation method. / Graduation date: 1972
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Sur l'attraction Sur la distribution de l'électricité sur deux sphères conductrices mises en présence /Alquier, Felix Gabriel Alexandre January 1900 (has links)
Thèse : Mécanique : Faculté des sciences de Paris : 1852. Thèse : Astronomie : Faculté des sciences de Paris : 1852. / Titre provenant de l'écran-titre.
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