Quasi-Static Brittle Fracture in Inhomogeneous Media and Iterated Conformal Maps: Modes I, II and III

The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require solution of the bi-Laplace rather than the Laplace equation. For all cases we can consider quenched randomness in the brittle material itself, as well as randomness in the succession of fracture events. While mode III calls for the advance (in time) of one analytic function, mode I and II call for the advance of two analytic functions. This fundamental difference creates different stress distribution around the cracks. As a result the geometric characteristics of the cracks differ, putting mode III in a different class compared to modes I and II.Comment: submitted to PRE For a version with qualitatively better figures see: http://www.weizmann.ac.il/chemphys/ander

Stress field around arbitrarily shaped cracks in two-dimensional elastic materials

The calculation of the stress field around an arbitrarily shaped crack in an infinite two-dimensional elastic medium is a mathematically daunting problem. With the exception of few exactly soluble crack shapes the available results are based on either perturbative approaches or on combinations of analytic and numerical techniques. We present here a general solution of this problem for any arbitrary crack. Along the way we develop a method to compute the conformal map from the exterior of a circle to the exterior of a line of arbitrary shape, offering it as a superior alternative to the classical Schwartz-Cristoffel transformation. Our calculation results in an accurate estimate of the full stress field and in particular of the stress intensity factors K_I and K_{II} and the T-stress which are essential in the theory of fracture.Comment: 7 pages, 4 figures, submitted for PR

Diffusion Limited Aggregation with Power-Law Pinning

Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth $R_N^{-\gamma}$ (where $R_N$ is the radius of the $N-$ particle cluster). For $\gamma > 1$ the growth pattern is in the same universality class as diffusion limited aggregation (DLA) growth, while for $\gamma < 1$ the resulting patterns have a lower fractal dimension $D(\gamma)$ than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at $\gamma = 1/2$, significantly smaller than might be expected from the lower bound $\alpha_{min} \simeq 0.67$ of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for $D(\gamma)$ both close to the breakdown of DLA universality class, i.e., $\gamma \lesssim 1$, and close to the pinning transition, i.e., $\gamma \gtrsim 1/2$.Comment: 5 pages, e figures, submitted to Phys. Rev.

New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps

We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth patterns are compared to those obtained by the best algorithms of direct numerical solutions. The fractal dimension of the patterns is discussed.Comment: Sumitted to Phys. Rev. Lett. Further details at http://www.pik-potsdam.de/~ander

Quasi-Static Fractures in Disordered Media and Iterated Conformal Maps

We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lam\'e equations without resorting to lattice models. Typical fracture patterns exhibit increased ramification due to the increase of the stress at the tips. We find the roughness exponent of the experimentally relevant backbone of the fracture pattern; it crosses over from about 0.5 for small scales to about 0.75 for large scales, in excellent agreement with experiments. We propose that this cross-over reflects the increased ramification of the fracture pattern.Comment: submitted to Physical Review Letter

Conformal mapping methods for interfacial dynamics

The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the article begins with an overview of continuous conformal-map dynamics. This includes problems of interfacial motion driven by harmonic fields (such as viscous fingering and void electromigration), bi-harmonic fields (such as viscous sintering and elastic pore evolution), and non-harmonic, conformally invariant fields (such as growth by advection-diffusion and electro-deposition). The second part of the article is devoted to iterated conformal maps for analogous problems in stochastic interfacial dynamics (such as diffusion-limited aggregation, dielectric breakdown, brittle fracture, and advection-diffusion-limited aggregation). The third part notes that all of these models can be extended to curved surfaces by an auxilliary conformal mapping from the complex plane, such as stereographic projection to a sphere. The article concludes with an outlook for further research.Comment: 37 pages, 12 (mostly color) figure

Salivary gland cancer in Southern Brazil: a prognostic study of 107 cases

Background: Salivary gland cancers (SGC) represent an uncommon group of heterogeneous tumors. We performed a retrospective survey of SGC diagnosed in a reference center for treatment of malignant tumors from the south of Brazil aiming to determine the prognostic value of demographic, clinic and pathologic features. Material and Methods: Cases diagnosed as SGC between 2006 and 2016 were retrospectively collected. Medical records were examined to extract demographic, clinic, pathologic and follow-up information. Results: One-hundred and seven cases of SGC were identified. The most common SGC were mucoepidermoid carcinoma (MEC) (n = 39) followed by adenoid cystic carcinoma (AdCC) (n = 29). Among AdCCs, 55.2% of cases were classified as cribriform, 27.6% as tubular and 17.2% as solid. The tubular subtype had the highest percentage of cases with perineural invasion (p=0.01). Among MEC, 61.5% of cases were classified as low grade, 15.4% as intermediate grade and 19.9% as high grade. Low grade MEC had the lowest percentage of cases with perineural invasion (p=0.04). The 5-year survival for loco-regional control, disease-free survival (DFS) and disease-specific survival were 75%, 70% and 84%, respectively. The following features were associated with poor DFS: advanced age (p=0.03), rural residency (p=0.01), being a smoker or former smoker (p=0.01), pain (p=0.03), nodal metastasis (p<0.001), need for chemotherapy (p=0.02), neck dissection (p=0.04), perineural invasion (p=0.01), and being diagnosed with AdCC compared to MEC (p=0.02). Conclusions: The clinco-demographic and pathologic features identified as prognostic factors reveal the profile of patients at increased risk of recurrence and who would benefit from closer follow-up

Disgust sensitivity relates to attitudes toward gay men and lesbian women across 31 nations

Previous work has reported a relation between pathogen-avoidance motivations and prejudice toward various social groups, including gay men and lesbian women. It is currently unknown whether this association is present across cultures, or specific to North America. Analyses of survey data from adult heterosexuals (N = 11,200) from 31 countries showed a small relation between pathogen disgust sensitivity (an individual-difference measure of pathogen-avoidance motivations) and measures of antigay attitudes. Analyses also showed that pathogen disgust sensitivity relates not only to antipathy toward gay men and lesbians, but also to negativity toward other groups, in particular those associated with violations of traditional sexual norms (e.g., prostitutes). These results suggest that the association between pathogen-avoidance motivations and antigay attitudes is relatively stable across cultures and is a manifestation of a more general relation between pathogen-avoidance motivations and prejudice towards groups associated with sexual norm violations

Human toxocariasis: contribution by Brazilian researchers

In the present paper the main aspects of the natural history of human infection by Toxocara larvae that occasionally result in the occurrence of visceral and/or ocular larva migrans syndrome were reviewed. The contribution by Brazilian researchers was emphasized, especially the staff of the Tropical Medicine Institute of São Paulo (IMT)