Sharp interface limit for a phase field model in structural optimization

We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse interface problem to a perimeter penalized sharp interface shape optimization problem in the sense of $\Gamma$-convergence of the reduced objective functional. Additionally, convergence of the equations of the first variation can be shown. The limit equations can also be derived directly from the problem in the sharp interface setting. Numerical computations demonstrate that the approach can be applied for complex structural optimization problems

Singular kernels, multiscale decomposition of microstructure, and dislocation models

We consider a model for dislocations in crystals introduced by Koslowski, Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel behaving as the $H^{1/2}$ norm of the slip. We obtain a sharp-interface limit of the model within the framework of $\Gamma$-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement argument no longer applies. Instead we show that the microstructure must be approximately one-dimensional on most length scales and exploit this property to derive a sharp lower bound

Analysis of an Inverse Problem Arising in Photolithography

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods.Comment: 28 pages, 1 figur

The chemical composition of the aerial parts essential oil of Acinos alpinus subsp. nebrodensis (Lamiaceae) growing in Sicily (Italy)

Acinos is a small genus of economically important plants belonging to Lamiaceae family whose botanical collocation is quite problematic due to the disagreement among the botanists and the presence in litera- ture of several names and synonyms from different sources. In the pre- sent study the chemical composition of the essential oil from aerial parts of Acinos alpinus subsp. nebrodensis (Strobl) Brullo & Brullo col- lected in Central Sicily was analyzed by GC-MS. The result showed the presence of large quantity of sesquiterpene hydrocarbons with germa- crene D (37.9%) as the most abundant component followed by (E)- b-caryophyllene (5.1%). Among the oxygenated monoterpenes thymol (8.3%) was the most abundant; good quantity of hexadecanoic acid (6.8%) was also observed. Chemotaxonomic considerations with respect all the other oils of Acinos taxa, studied so far, were carried out

Extracellular vesicles in airway homeostasis and pathophysiology

The epithelial–mesenchymal trophic unit (EMTU) is a morphofunctional entity involved in the maintenance of the homeostasis of airways as well as in the pathogenesis of several diseases, including asthma and chronic obstructive pulmonary disease (COPD). The “muco-microbiotic layer” (MML) is the innermost layer of airways made by microbiota elements (bacteria, viruses, archaea and fungi) and the surrounding mucous matrix. The MML homeostasis is also crucial for maintaining the healthy status of organs and its alteration is at the basis of airway disorders. Nanovesicles produced by EMTU and MML elements are probably the most important tool of communication among the different cell types, including inflammatory ones. How nanovesicles produced by EMTU and MML may affect the airway integrity, leading to the onset of asthma and COPD, as well as their putative use in therapy will be discussed here

Phase field approach to optimal packing problems and related Cheeger clusters

In a fixed domain of $\Bbb{R}^N$ we study the asymptotic behaviour of optimal clusters associated to $\alpha$-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter $\alpha$ converges to the "critical" value $\Big (\frac{N-1}{N}\Big ) _+$, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute $\alpha$-Cheeger constants, optimal clusters and, as a consequence of the asymptotic result, optimal packings. Numerical experiments are carried over in two and three space dimensions

A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions

In this paper we study a simple non-local semilinear parabolic equation with Neumann boundary condition. We give local existence result and prove global existence for small initial data. A natural non increasing in time energy is associated to this equation. We prove that the solution blows up at finite time $T$ if and only if its energy is negative at some time before $T$. The proof of this result is based on a Gamma-convergence technique

The Mediterranean island states : Malta and Cyprus

The 2004 European Union enlargement also included the Mediterranean island-states of Cyprus and Malta, two former British colonies and members of the British Commonwealth. The islands share a number of similarities but they are also dissimilar in uniquely distinct ways. The membership applications of both states initially presented the EU with a number of political difficulties. With respect to Cyprus, many member states would have preferred to see the island join the Union after the ‘Cyprus Problem’ had been settled. As for Malta, the island showed a very high degree of Euroskepticism. It froze its application in 1996 but reactivated it in 1998. Apart from this skepticism the island’s neutral status, enshrined in the Constitution could present insurmountable problems.peer-reviewe

A study of methyl formate in astrochemical environments

Several complex organic molecules are routinely detected in high abundances towards hot cores and hot corinos. For many of them, their paths of formation in space are uncertain, as gas phase reactions alone seem to be insufficient. In this paper, we investigate a possible solid-phase route of formation for methyl formate (HCOOCH3). We use a chemical model updated with recent results from an experiment where simulated grain surfaces were irradiated with 200 keV protons at 16 K, to simulate the effects of cosmic ray irradiation on grain surfaces. We find that this model may be sufficient to reproduce the observed methyl formate in dark clouds, but not that found in hot cores and corinos.Comment: 6 pages, 2 figures, 2 tables Accepted by MNRA