Optimal regularity and structure of the free boundary for minimizers in cohesive zone models

We study optimal regularity and free boundary for minimizers of an energy functional arising in cohesive zone models for fracture mechanics. Under smoothness assumptions on the boundary conditions and on the fracture energy density, we show that minimizers are $C^{1, 1/2}$, and that near non-degenerate points the fracture set is $C^{1, \alpha}$, for some $\alpha \in (0, 1)$.Comment: 39 page

A second order minimality condition for the Mumford-Shah functional

A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\Gamma)$, $\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.Comment: 30 page

Linearly constrained evolutions of critical points and an application to cohesive fractures

We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite dimension, is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite dimensional. Nevertheless, in the infinite dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discrete-to-continuum limit. We show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we provide several numerical experiments both in one and two dimensions. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material

Rapid evolution of female-biased genes among four species of Anopheles malaria mosquitoes.

Understanding how phenotypic differences between males and females arise from the sex-biased expression of nearly identical genomes can reveal important insights into the biology and evolution of a species. Among Anopheles mosquito species, these phenotypic differences include vectorial capacity, as it is only females that blood feed and thus transmit human malaria. Here, we use RNA-seq data from multiple tissues of four vector species spanning the Anopheles phylogeny to explore the genomic and evolutionary properties of sex-biased genes. We find that, in these mosquitoes, in contrast to what has been found in many other organisms, female-biased genes are more rapidly evolving in sequence, expression, and genic turnover than male-biased genes. Our results suggest that this atypical pattern may be due to the combination of sex-specific life history challenges encountered by females, such as blood feeding. Furthermore, female propensity to mate only once in nature in male swarms likely diminishes sexual selection of post-reproductive traits related to sperm competition among males. We also develop a comparative framework to systematically explore tissue- and sex-specific splicing to document its conservation throughout the genus and identify a set of candidate genes for future functional analyses of sex-specific isoform usage. Finally, our data reveal that the deficit of male-biased genes on the X Chromosomes in Anopheles is a conserved feature in this genus and can be directly attributed to chromosome-wide transcriptional regulation that de-masculinizes the X in male reproductive tissues

A comparison of delamination models: Modeling, properties, and applications

This contribution presents recent results in the modeling and the analysis of delamination problems. It addresses adhesive contact, brittle, and cohesive zone models both in a quasistatic and a viscous, dynamic setting for the bulk part. Also different evolution laws for the delaminating surface are discussed

Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We discover the appearance of the initial layers, which appear naturally when we consider the systems with different initial data and analyze them rigorously. In particular, we obtain matched asymptotic solutions of the systems and rate of convergence. We also investigate properties of the effective Hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations.Comment: final version, to appear in Arch. Ration. Mech. Ana

Inflammatory myofibroblastic tumor after lung transplant-A rare and aggressive complication. A case report.

Introduction Malignant diseases are well-known complications after lung transplantation (LT). Among these, inflammatory myofibroblastic tumor (IMT) is a rare neoplasm with a not well-known and often aggressive biological behavior. Material and Methods We hereby describe 2 cases of cystic fibrosis patients who underwent bilateral sequential LT (BSLT) complicated by IMT. Results A 26-year-old man presented a right endobronchial lesion 6 months after BSLT. Two consecutive fiber bronchoscopic biopsies showed granulation tissue. For the persistent lesion growth, the patient underwent a transthoracic biopsy showing histologic diagnosis of IMT. Therefore, he underwent to right pneumonectomy that was unfortunately complicated after 6 months with a late bronchopleural fistula and empyema with exitus 6 months later. A 31-year-old woman 1 year after BSLT presented with a left voluminous pleural-parenchymal lesion; the histologic examination after biopsy revealed an IMT. She underwent a removal of the lesion with a macroscopic R0 resection. Histologic, immunophenotypic, and cytogenetic examinations showed a strong overexpression of anaplastic lymphoma kinase requiring biological adjuvant therapies; however, the patient refused it. Four years later, she presented a recurrence treated with debulking procedure and adjuvant radiotherapy. At last follow-up, the patient was alive with stable disease and optimal graft function. Conclusions Although IMT is a rare complication after lung transplant, to obtain a careful diagnosis, an early and aggressive treatment is mandatory

Radical remodeling of the Y chromosome in a recent radiation of malaria mosquitoes

open28openHall A.B.; Papathanos P.-A.; Sharma A.; Cheng C.; Akbari O.S.; Assour L.; Bergman N.H.; Cagnetti A.; Crisanti A.; Dottorini T.; Fiorentini E.; Galizi R.; Hnath J.; Jiang X.; Koren S.; Nolan T.; Radune D.; Sharakhova M.V.; Steele A.; Timoshevskiy V.A.; Windbichler N.; Zhang S.; Hahn M.W.; Phillippy A.M.; Emrich S.J.; Sharakhov I.V.; Tu Z.J.; Besansky N.J.Hall, A. B.; Papathanos, P. -A.; SHARMA DHAKAL, Apsara; Cheng, C.; Akbari, O. S.; Assour, L.; Bergman, N. H.; Cagnetti, A.; Crisanti, A.; Dottorini, T.; Fiorentini, E.; Galizi, R.; Hnath, J.; Jiang, X.; Koren, S.; Nolan, T.; Radune, D.; Sharakhova, M. V.; Steele, A.; Timoshevskiy, V. A.; Windbichler, N.; Zhang, Shangu; Hahn, M. W.; Phillippy, A. M.; Emrich, S. J.; Sharakhov, I. V.; Tu, Z. J.; Besansky, N. J

Quasistatic delamination of sandwich-like Kirchhoff-Love plates

A quasistatic rate-independent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rate-independent delamination model for a laminated Kirchhoff-Love plate is obtained as limit of these quasistatic processes. The same dimension reduction procedure is eventually applied to processes which are sensitive to delamination modes, namely opening vs. shearing is distinguishe