Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

Scalable In Situ Hybridization on Tissue Arrays for Validation of Novel Cancer and Tissue-Specific Biomarkers

Tissue localization of gene expression is increasingly important for accurate interpretation of large scale datasets from expression and mutational analyses. To this end, we have (1) developed a robust and scalable procedure for generation of mRNA hybridization probes, providing >95% first-pass success rate in probe generation to any human target gene and (2) adopted an automated staining procedure for analyses of formalin-fixed paraffin-embedded tissues and tissue microarrays. The in situ mRNA and protein expression patterns for genes with known as well as unknown tissue expression patterns were analyzed in normal and malignant tissues to assess procedure specificity and whether in situ hybridization can be used for validating novel antibodies. We demonstrate concordance between in situ transcript and protein expression patterns of the well-known pathology biomarkers KRT17, CHGA, MKI67, PECAM1 and VIL1, and provide independent validation for novel antibodies to the biomarkers BRD1, EZH2, JUP and SATB2. The present study provides a foundation for comprehensive in situ gene set or transcriptome analyses of human normal and tumor tissues

The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts

The impact of non-Gaussian height distribution and spectral properties on the lubrication performance of counterformal (point) contacts is quantitatively studied (film parameter, Λ, and asperity load ratio, La) by developing a mixed lubrication model. The Weibull height distribution function and power spectral density (PSD) are used to generate artificial surface topographies (non-Gaussian and Gaussian, isotropic), as these surface topographies are found in many tribological components. The set of variables needed to parametrize and their effect on mixed lubrication is discussed, including the shape parameter, the autocorrelation length, the wavelength ratio, and the Hurst coefficient. It is revealed that a rough surface with a lower shape parameter exhibits higher hydrodynamic lift. The spectral properties (the autocorrelation length and the wavelength ratio) of rough surfaces significantly affect the film parameter and the hydrodynamic and asperity pressures. The film parameter is slightly influenced by the Hurst coefficient.Validerad;2024;Nivå 2;2024-04-03 (hanlid);Full text license: CC BY 4.0</p

The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts

The impact of non-Gaussian height distribution and spectral properties on the lubrication performance of counterformal (point) contacts is quantitatively studied (film parameter, Λ, and asperity load ratio, La) by developing a mixed lubrication model. The Weibull height distribution function and power spectral density (PSD) are used to generate artificial surface topographies (non-Gaussian and Gaussian, isotropic), as these surface topographies are found in many tribological components. The set of variables needed to parametrize and their effect on mixed lubrication is discussed, including the shape parameter, the autocorrelation length, the wavelength ratio, and the Hurst coefficient. It is revealed that a rough surface with a lower shape parameter exhibits higher hydrodynamic lift. The spectral properties (the autocorrelation length and the wavelength ratio) of rough surfaces significantly affect the film parameter and the hydrodynamic and asperity pressures. The film parameter is slightly influenced by the Hurst coefficient.Validerad;2024;Nivå 2;2024-04-03 (hanlid);Full text license: CC BY 4.0</p