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Analytical expressions for the vector magnetic fields and Fourier transforms associated with thin film heads are presented. These results are derived from accurate, approximate expressions for the surface field of an asymmetric thin film head determined from conformal mapping solutions. A 2-dimensional Green's function is integrated to yield exact analytic expressions for the fields, which are of no more complexity than the Karlqvist field approximations. In spite of their simplicity, these expressions accurately represent the fields at all corners, both at the gap and at the pole edges. These results are only approximate at spatial distances beyond the head edges and at wavelengths beyond about ten times the total head length. The Fourier transform of the surface field is also given in simple analytic form. As an example of the use of these expressions, it is shown how the effect of pole length to gap length ratio, p/g, on pulse superposition can be easily estimated.

Eshelby showed that the pointwise force F on and normal to the interface between a transformed inclusion and its surrounding matrix is the jump in the normal component of the elastic energy-momentum tensor across the interface. Gavazza later showed, using an entirely different approach, that this thermodynamic driving force F has a much simpler form involving only the average of the stress tensors at adjacent points on opposite sides of the interface and the “transformation strain” tensor. The equivalence of and connection between the two formulae was apparently first shown by Eshelby in a personal letter to Gavazza (attached as an appendix to this paper), although the brevity of the letter makes following Eshelby’s proof a little difficult. Here we expand Eshelby’s hitherto unpublished proof of the equivalence of the two expressions in what we believe is a clearer fashion. [ABSTRACT FROM AUTHOR]

The existence of Eshelby’s equivalent inclusion solution is proved for a non-degenerate ‘transformed’ ellipsoidal inhomogeneity in an infinite anisotropic linear elastic matrix. We prove the invertibility of the fourth rank tensor expression, C′SE+C(I−SE), where C is the stiffness tensor of the matrix, C′ is the stiffness tensor of the inhomogeneity, I is the Eshelby tensor, and SE is the symmetric identity tensor. Taking advantage of the positive definiteness of certain tensor expressions, a proof-by-contradiction using energy arguments is posited that eliminates the possibility that the above expression is singular. Because the tensor expression is non-singular, it can always be inverted and Eshelby’s equivalent ellipsoidal inclusion method can be used to find the stress and strain fields in both the matrix and inhomogeneity. [ABSTRACT FROM PUBLISHER]

Kelvin probe force microscopy (KPFM) is designed for measuring the tip-sample contact potential differences by probing the sample surface, measuring the electrostatic interaction, and adjusting a feedback circuit. However, for the case of a dielectric (insulating) sample, the contact potential difference may be ill defined, and the KPFM probe may be sensing electrostatic interactions with a certain distribution of sample trapped charges or dipoles, leading to difficulty in interpreting the images. We have proposed a general framework based on boundary integral equations for simulating the KPFM image based on the knowledge about the sample charge distributions (forward problem) and a deconvolution algorithm solving for the trapped charges on the surface from an image (inverse problem). The forward problem is a classical potential problem, which can be efficiently solved using the boundary element method. Nevertheless, the inverse problem is ill posed due to data incompleteness. For some special cases, we have developed deconvolution algorithms based on the forward problem solution. As an example, this algorithm is applied to process the KPFM image of a gadolinia-doped ceria thin film to solve for its surface charge density, which is a more relevant quantity for samples of this kind than the contact potential difference (normally only defined for conductive samples) values contained in the raw image. [ABSTRACT FROM AUTHOR]

Presents the thermal management options which have been evaluated in the development of the multifunctional structure (MFS) designs for miniature spacecraft. MFS thermal control aspects; Thermal analysis and vacuum testing of MFS panels; MFS panel configuration.

The capacitance system of a hyperboloidal tip and a rough surface is usually encountered in analyzing electrostatic force microscopy images. In this letter, a perturbation approach has been applied to solve for the electric potential of this system, in which the rough surface is treated as perturbation from a flat one. For the first-variation solution, the boundary value problem is represented in the prolate-spheroidal coordinate system and solved in terms of a generalized Fourier series involving conical functions. Based on this solution, the tip-surface Coulombic interaction can be computed. Sample calculations have been applied to sinusoidal surface profiles. [ABSTRACT FROM AUTHOR]

A preface to this special issue of "Mathematics and Mechanics of Solids," which is devoted to topical problems in the theory and applications of linear elasticity, is presented.

This study compared human and monkey sensitivity to the English liquid /ra-la/ contrast using a low-uncertainty repeating-standard discrimination procedure. A synthetic continuum was constructed by varying both a spectral cue in the third formant (F3 onset frequency) and a temporal cue in the first formant (steady-state period before the F1 transition into the vowel). In experiment 1, differential sensitivity was measured using both the /ra/ and /la/ ends of the continuum as standards. Humans were less sensitive than monkeys to variation at the /ra/ end, but equally sensitive at the /la/ end. In experiment 2, subjects were presented with pairwise comparisons from the continuum to discriminate. Human discrimination was best at the identified phoneme boundary near the center of the continuum, while monkey discrimination was best inside the /ra/ category. These results indicate qualitative differences between human and monkey discrimination of this continuum: categorical-like for humans, and noncategorical for monkeys. [Work supported by NIDCD.] [ABSTRACT FROM AUTHOR]

Electrostatic force microscopy (EFM) is a special design of non-contact atomic force microscopy used for detecting electrostatic interactions between the probe tip and the sample. Its resolution is limited by the finite probe size and the long-range characteristics of electrostatic forces. Therefore, quantitative analysis is crucial to understanding the relationship between the actual local surface potential distribution and the quantities obtained from EFM measurements. To study EFM measurements on bimetallic samples with surface potential inhomogeneities as a special case, we have simulated such measurements using the boundary element method and calculated the force component and force gradient component that would be measured by amplitude modulation (AM) EFM and frequency modulation (FM) EFM, respectively. Such analyses have been performed for inhomogeneities of various shapes and sizes, for different tip-sample separations and tip geometries, for different applied voltages, and for different media (e.g., vacuum or water) in which the experiment is performed. For a sample with a surface potential discontinuity, the FM-EFM resolution expression agrees with the literature; however, the simulation for AM-EFM suggests the existence of an optimal tip radius of curvature in terms of resolution. On the other hand, for samples with strip- and disk-shaped surface potential inhomogeneities, we have obtained quantitative expressions for the detectability size requirements as a function of experimental conditions for both AM- and FM-EFMs, which suggest that a larger tip radius of curvature is moderately favored for detecting the presence of such inhomogeneities.