Non-local fractional derivatives. Discrete and continuous

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When the functions are good enough, these approximation procedures give a measure of the order of approximation. These results also allows us to prove the coincidence, for good enough functions, of the Marchaud and Gr\"unwald-Letnikov derivatives in every point and the speed of convergence to the Gr\"unwald-Letnikov derivative. The fractional discrete derivative will be also described as a Neumann-Dirichlet operator defined by a semi-discrete extension problem. Some operators related to the Harmonic Analysis associated to the discrete derivative will be also considered, in particular their behavior in the Lebesgue spaces $\ell^p(\mathbb{Z}).

Thermal boundary resistance at Si/Ge interfaces determined by approach-to-equilibrium molecular dynamics simulations

The thermal boundary resistance of Si/Ge interfaces as been determined using approach-to-equilibrium molecular dynamics simulations. Assuming a reciprocal linear dependence of the thermal boundary resistance, a length-independent bulk thermal boundary resistance could be extracted from the calculation resulting in a value of 3.76x10$^{-9}$ m$^2$ K/W for a sharp Si/Ge interface and thermal transport from Si to Ge. Introducing an interface with finite thickness of 0.5 nm consisting of a SiGe alloy, the bulk thermal resistance slightly decreases compared to the sharp Si/Ge interface. Further growth of the boundary leads to an increase in the bulk thermal boundary resistance. When the heat flow is inverted (Ge to Si), the thermal boundary resistance is found to be higher. From the differences in the thermal boundary resistance for different heat flow direction, the rectification factor of the Si/Ge has been determined and is found to significantly decrease when the sharp interface is moderated by introduction of a SiGe alloy in the boundary layer.Comment: 7 pages, 6 figure

Challenging the paradigm of singularity excision in gravitational collapse

A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing three-dimensional simulations of the collapse of uniformly rotating stars to black holes without excision. We show that this choice, combined with suitable gauge conditions and the use of minute numerical dissipation, improves dramatically the long-term stability of the evolutions. In turn, this allows for the calculation of the waveforms well beyond what previously possible, providing information on the black-hole ringing and setting a new mark on the present knowledge of the gravitational-wave emission from the stellar collapse to a rotating black hole.Comment: 4 pages, 4 figures, accepted for publication on Phys. Rev. Let

Redox control of multidrug resistance and Its possible modulation by antioxidants

Clinical efficacy of anticancer chemotherapies is dramatically hampered by multidrug resistance (MDR) dependent on inherited traits, acquired defence against toxins, and adaptive mechanisms mounting in tumours. There is overwhelming evidence that molecular events leading to MDR are regulated by redox mechanisms. For example, chemotherapeutics which overrun the first obstacle of redox-regulated cellular uptake channels (MDR1, MDR2, and MDR3) induce a concerted action of phase I/II metabolic enzymes with a temporal redox-regulated axis. This results in rapid metabolic transformation and elimination of a toxin. This metabolic axis is tightly interconnected with the inducible Nrf2-linked pathway, a key switch-on mechanism for upregulation of endogenous antioxidant enzymes and detoxifying systems. As a result, chemotherapeutics and cytotoxic by-products of their metabolism (ROS, hydroperoxides, and aldehydes) are inactivated and MDR occurs. On the other hand, tumour cells are capable of mounting an adaptive antioxidant response against ROS produced by chemotherapeutics and host immune cells. The multiple redox-dependent mechanisms involved in MDR prompted suggesting redox-active drugs (antioxidants and prooxidants) or inhibitors of inducible antioxidant defence as a novel approach to diminish MDR. Pitfalls and progress in this direction are discussed