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

Continuous-variable quantum probes for structured environments

We address parameter estimation for structured environments and suggest an effective estimation scheme based on continuous-variables quantum probes. In particular, we investigate the use of a single bosonic mode as a probe forOhmic reservoirs, and obtain the ultimate quantum limits to the precise estimation of their cutoff frequency. We assume the probe prepared in a Gaussian state and determine the optimal working regime, i.e., the conditions for the maximization of the quantum Fisher information in terms of the initial preparation, the reservoir temperature, and the interaction time. Upon investigating the Fisher information of feasible measurements, we arrive at a remarkable simple result: homodyne detection of canonical variables allows one to achieve the ultimate quantum limit to precision under suitable, mild, conditions. Finally, upon exploiting a perturbative approach, we find the invariant sweet spots of the (tunable) characteristic frequency of the probe, able to drive the probe towards the optimal working regime

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

The Italian document: decisions for intensive care when there is an imbalance between care needs and resources during the COVID-19 pandemic

Background: In early 2020, the Italian Society of Anesthesia Analgesia Resuscitation and Intensive Care (SIAARTI) published clinical ethics recommendations for the allocation of intensive care during COVID-19 pandemic emergency. Later the Italian National Institute of Health (ISS) invited SIAARTI and the Italian Society of Legal and Insurance Medicine to prepare a draft document for the definition of triage criteria for intensive care during the emergency, to be implemented in case of complete saturation of care resources. Methods: Following formal methods, including two Delphi rounds, a multidisciplinary group with expertise in intensive care, legal medicine and law developed 12 statements addressing: (1) principles and responsibilities; (2) triage; (3) previously expressed wishes; (4) reassessment and shifting to palliative care; (5) collegiality and transparency of decisions. The draft of the statements, with their explanatory comments, underwent a public consultation opened to Italian scientific or technical-professional societies and other stakeholders (i.e., associations of citizens, patients and caregivers; religious communities; industry; public institutions; universities and research institutes). Individual healthcare providers, lay people, or other associations could address their comments by e-mail. Results: Eight stakeholders (including scientific societies, ethics organizations, and a religious community), and 8 individuals (including medical experts, ethicists and an association) participated to the public consultation. The stakeholders’ agreement with statements was on average very high (ranging from 4.1 to 4.9, on a scale from 1—full disagreement to 5—full agreement). The 4 statements concerning triage stated that in case of saturation of care resources, the intensive care triage had to be oriented to ensuring life-sustaining treatments to as many patients as possible who could benefit from them. The decision should follow full assessment of each patient, taking into account comorbidities, previous functional status and frailty, current clinical condition, likely impact of intensive treatment, and the patient's wishes. Age should be considered as part of the global assessment of the patient. Conclusions: Lacking national guidelines, the document is the reference standard for healthcare professionals in case of imbalance between care needs and available resources during a COVID-19 pandemic in Italy, and a point of reference for the medico-legal assessment in cases of dispute

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

Hypercoagulability of COVID-19 patients in Intensive Care Unit: A Report of Thromboelastography Findings and other Parameters of Hemostasis

BACKGROUND: The severe inflammatory state secondary to Covid-19 leads to a severe derangement of hemostasis that has been recently described as a state of disseminated intravascular coagulation (DIC) and consumption coagulopathy, defined as decreased platelet count, increased fibrin(ogen) degradation products such as D-dimer as well as low fibrinogen. AIMS: Whole blood from 24 patients admitted at the intensive care unit because of Covid-19 was collected and evaluated with thromboelastography by the TEG point-of-care device on a single occasion and six underwent repeated measurements on two consecutive days for a total of 30 observations. Plasma was evaluated for the other parameters of hemostasis. RESULTS: TEG parameters are consistent with a state of hypercoagulability as shown by decreased R and K values, and increased values of K angle and MA. Platelet count was normal or increased, prothrombin time and activated partial thromboplastin time were near(normal). Fibrinogen was increased and D-dimer was dramatically increased. C-reactive protein was increased. Factor VIII and von Willebrand factor (n=11) were increased. Antithrombin (n=11) was marginally decreased and protein C (n=11) was increased. CONCLUSION: The results of this cohort of patients with Covid-19 are not consistent with acute DIC, rather they support hypercoagulability together with a severe inflammatory state. These findings may explain the events of venous thromboembolism observed in some of these patients and support antithrombotic prophylaxis/treatment. Clinical trials are urgently needed to establish the type of drug, dosage and optimal duration of prophylaxis

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