Inaug-diss.--Tübingen.

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

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

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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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

Thèse : Mécanique : Faculté des sciences de Paris : 1852. Thèse : Astronomie : Faculté des sciences de Paris : 1852. / Titre provenant de l'écran-titre.