Discontinuous Galerkin approximation of linear parabolic problems with dynamic boundary conditions

In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete scheme. More precisely, using polynomials of degree $p\geq 1$ on meshes with granularity $h$ along with a backward Euler time-stepping scheme with time-step $\Delta t$, we prove that the fully-discrete solution is bounded by the data and it converges, in a suitable (mesh-dependent) energy norm, to the exact solution with optimal order $h^p + \Delta t$. The sharpness of the theoretical estimates are verified through several numerical experiments

Oxidation States, Thouless' Pumps, and Nontrivial Ionic Transport in Nonstoichiometric Electrolytes

Thouless' quantization of adiabatic particle transport permits one to associate an integer topological charge with each atom of an electronically gapped material. If these charges are additive and independent of atomic positions, they provide a rigorous definition of atomic oxidation states and atoms can be identified as integer-charge carriers in ionic conductors. Whenever these conditions are met, charge transport is necessarily convective; i.e., it cannot occur without substantial ionic flow, a transport regime that we dub trivial. We show that the topological requirements that allow these conditions to be broken are the same that would determine a Thouless' pump mechanism if the system were subject to a suitably defined time-periodic Hamiltonian. The occurrence of these requirements determines a nontrivial transport regime whereby charge can flow without any ionic convection, even in electronic insulators. These results are first demonstrated with a couple of simple molecular models that display a quantum-pump mechanism upon introduction of a fictitious time dependence of the atomic positions along a closed loop in configuration space. We finally examine the impact of our findings on the transport properties of nonstoichiometric alkali-halide melts, where the same topological conditions that would induce a quantum-pump mechanism along certain closed loops in configuration space also determine a nontrivial transport regime such that most of the total charge current results to be uncorrelated from the ionic ones

Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D

In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier-Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered.Comment: 32 page

Consteel© EAF and conventional EAF: a comparison in maintenance practices

The present paper highlights the main differences between Consteel® and conventional EAF technologiesregarding scheduled and unscheduled maintenance practices. The study has been made on the basis of datacollected in plants with high maintenance standards and more than 10 years of operational experience.These data have been analyzed and organized in a comparison table where they have been associated with therelevant maintenance costs. The comparison shows that the Consteel® technology achieves a significantreduction in the overall maintenance costs compared to a conventional EAF

Granular Elasticity without the Coulomb Condition

An self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.Comment: 4pages, 2 figure

Silybin counteracts lipid excess and oxidative stress in cultured steatotic hepatic cells

AIM: To investigate in vitro the therapeutic effect and mechanisms of silybin in a cellular model of hepatic steatosis. METHODS: Rat hepatoma FaO cells were loaded with lipids by exposure to 0.75 mmol/L oleate/palmitate for 3 h to mimic liver steatosis. Then, the steatotic cells were incubated for 24 h with different concentrations (25 to 100 mol/L) of silybin as phytosome complex with Vitamin E. The effects of silybin on lipid accumulation and metabolism, and on indices of oxidative stress were evaluated by absorption and fluorescence microscopy, quantitative real-time PCR, Western blot, spectrophotometric and fluorimetric assays. RESULTS: Lipid-loading resulted in intracellular triglyceride (TG) accumulation inside lipid droplets, whose number and size increased. TG accumulation was mediated by increased levels of peroxisome proliferator-activated receptors (PPARs) and sterol regulatory element-binding protein-1c (SREBP-1c). The lipid imbalance was associated with higher production of reactive oxygen species (ROS) resulting in increased lipid peroxidation, stimulation of catalase activity and activation of nuclear factor kappa-B (NF-B). Incubation of steatotic cells with silybin 50 mol/L significantly reduced TG accumulation likely by promoting lipid catabolism and by inhibiting lipogenic pathways, as suggested by the changes in carnitine palmitoyltransferase 1 (CPT-1), PPAR and SREBP-1c levels. The reduction in fat accumulation exerted by silybin in the steatotic cells was associated with the improvement of the oxidative imbalance caused by lipid excess as demonstrated by the reduction in ROS content, lipid peroxidation, catalase activity and NF-B activation

3,5-Diiodo-L-thyronine modulates the expression of genes of lipid metabolism in a rat model of fatty liver.

Recent reports demonstrated that 3,5-diiodo-l-thyronine (T(2)) was able to prevent lipid accumulation in the liver of rats fed a high-fat diet (HFD). In this study, we investigated how the rat liver responds to HFD and T(2) treatment by assessing the transcription profiles of some genes involved in the pathways of lipid metabolism: oxidation, storage and secretion. The mRNA levels of the peroxisome proliferator-activated receptors (PPARα, PPARγ and PPARδ), and of their target enzymes acyl-CoA oxidase and stearoyl-CoA desaturase were evaluated by real-time RT-PCR. Moreover, the expression of the adipose triglyceride lipase involved in lipid mobilisation, of the main PAT proteins acting in lipid droplet (LD) turnover, and of apoprotein B (apo B), the major protein component of very low-density lipoproteins (VLDLs) were analysed. Overall, our data demonstrated that T(2) administration to HFD rats counteracts most of the hepatic transcriptional changes that occurred in response to the excess exogenous fat. In particular, our results suggest that T(2) may prevent the pathways leading to lipid storage in LDs, promote the processes of lipid mobilisation from LDs and secretion as VLDL, in addition to the stimulation of pathways of lipid oxidation. In conclusion, our findings might give an insight into the mechanisms underlying the anti-steatotic ability of T(2) and help to define the potential therapeutic role of T(2) for preventing or treating liver steatosis

A Hedged Monte Carlo Approach to Real Option Pricing

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or subjective) measure in a possibly incomplete market. Our approach is suitable also to incorporating subjective views from management or market experts and to stochastic investment costs. It is based on the Hedged Monte Carlo strategy proposed by Potters et al (2001) where options are priced simultaneously with the determination of the corresponding hedging. The approach is particularly well-suited to the evaluation of commodity related projects whereby the availability of pricing formulae is very rare, the scenario simulations are usually available only in the historical measure, and the cash flows can be highly nonlinear functions of the prices.Comment: 25 pages, 14 figure