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

Rank-(n – 1) convexity and quasiconvexity for divergence free fields

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Convergence of nonlocal threshold dynamics approximations to front propagation

In this note we prove that appropriately scaled threshold dynamics-type algorithms corresponding to the fractional Laplacian of order $\alpha \in (0,2)$ converge to moving fronts. When $\alpha \geqq 1$ the resulting interface moves by weighted mean curvature, while for $\alpha <1$ the normal velocity is nonlocal of ``fractional-type.'' The results easily extend to general nonlocal anisotropic threshold dynamics schemes.Comment: 19 page

Stem cells and physical energies: can we really drive stem cell fate?

Adult stem cells are undifferentiated elements able to self-renew or differentiate to maintain tissue integrity. Within this context, stem cells are able to divide in a symmetric fashion, feature characterising all the somatic cells, or in an asymmetric way, which leads daughter cells to different fates. It is worth highlighting that cell polarity have a critical role in regulating stem cell asymmetric division and the proper control of cell division depends on different proteins involved in cell development, differentiation and maintenance of tissue homeostasis. Moreover, the interaction between cells and the extracellular matrix are crucial in influencing cell behavior, included in terms of mechanical properties as cytoskeleton plasticity and remodelling, and membrane tension. Finally, the activation of specific transcriptional program and epigenetic modifications contributes to cell fate determination, through modulation of cellular signalling cascades. It is well known that physical and mechanical stimuli are able to influence biological systems, and in this context, the effects of electromagnetic fields (EMFs) have already shown a considerable role, even though there is a lack of knowledge and much remains to be done around this topic. In this review, we summarize the historical background of EMFs applications and the main molecular mechanism involved in cellular remodelling, with particular attention to cytoskeleton elasticity and cell polarity, required for driving stem cell behavior

Inverse optical tomography through PDE constrained optimisation in L∞

Fluorescent Optical Tomography (FOT) is a new bio-medical imaging method with wider industrial applications. It is currently intensely researched since it is very precise and with no side effects for humans, as it uses non-ionising red and infrared light. Mathematically, FOT can be modelled as an inverse parameter identification problem, associated with a coupled elliptic system with Robin boundary conditions. Herein we utilise novel methods of Calculus of Variations in L∞ to lay the mathematical foundations of FOT which we pose as a PDE-constrained minimisation problem in Lp and L∞

Unravelling cellular mechanisms of stem cell senescence: An aid from natural bioactive molecules

Cellular senescence plays a role in the onset of age-related pathologies and in the loss of tissue homeostasis. Natural compounds of food or plants exert an important antioxidant activity, counteracting the formation of harmful free radicals. In the presence of an intense stressing event, cells activate specific responses to counteract senescence or cell death. In the present paper, we aimed at evaluating the levels of expression of specific markers of senescence, in order to demonstrate that extracts from Myrtus Communis L. can prevent premature senescence in ADSCs exposed to oxidative stress. Cells were cultured in the presence of Myrtus extracts for 12–24 and 48 h and then incubated with H2O2 to induce senescence. We then evaluated the expression of senescence-related markers p16, p19, p21, p53, TERT, c-Myc, and the senescence-associated β-Galactoidase activity. Our results showed that pre-treatment with Myrtus extracts protects cells from premature senescence, by regulating the cell cycle, and inducing the expression of TERT and c-Myc. These findings suggest a potential application of these natural compounds in the prevention and treatment of various diseases, counteracting premature senescence and preserving tissue functions

Solid state hydrogen storage in alanates and alanate-based compounds: A review

The safest way to store hydrogen is in solid form, physically entrapped in molecular form in highly porous materials, or chemically bound in atomic form in hydrides. Among the different families of these compounds, alkaline and alkaline earth metals alumino-hydrides (alanates) have been regarded as promising storing media and have been extensively studied since 1997, when Bogdanovic and Schwickardi reported that Ti-doped sodium alanate could be reversibly dehydrogenated under moderate conditions. In this review, the preparative methods; the crystal structure; the physico-chemical and hydrogen absorption-desorption properties of the alanates of Li, Na, K, Ca, Mg, Y, Eu, and Sr; and of some of the most interesting multi-cation alanates will be summarized and discussed. The most promising alanate-based reactive hydride composite (RHC) systems developed in the last few years will also be described and commented on concerning their hydrogen absorption and desorption performance