Preconditioning strategies for the numerical solution of convection-diffusion partial differential equations

Il trattamento numerico dell'equazione di convezione-diffusione con le relative condizioni al bordo, comporta la risoluzione di sistemi lineari algebrici di grandi dimensioni in cui la matrice dei coefficienti è non simmetrica. Risolutori iterativi basati sul sottospazio di Krylov sono ampiamente utilizzati per questi sistemi lineari la cui risoluzione risulta particolarmente impegnativa nel caso di convezione dominante. In questa tesi vengono analizzate alcune strategie di precondizionamento, atte ad accelerare la convergenza di questi metodi iterativi. Vengono confrontati sperimentalmente precondizionatori molto noti come ILU e iterazioni di tipo inner-outer flessibile. Nel caso in cui i coefficienti del termine di convezione siano a variabili separabili, proponiamo una nuova strategia di precondizionamento basata sull'approssimazione, mediante equazione matriciale, dell'operatore differenziale di convezione-diffusione. L'azione di questo nuovo precondizionatore sfrutta in modo opportuno recenti risolutori efficienti per equazioni matriciali lineari. Vengono riportati numerosi esperimenti numerici per studiare la dipendenza della performance dei diversi risolutori dalla scelta del termine di convezione, e dai parametri di discretizzazione.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Doubly-charged ethane ions: Solution to the dilemma of stability predicted by theory and instability observed in experiment

Potential energy curves have been computed for [C2H6]2+ ions and the results used to interpret the conspicuous absence of these ions in 2E mass spectra and in charge-stripping experiments. The energies and structures of geometry-optimized ground-state singlet and excited-state triplet [C2H6]2+ ions have been determined along with energies for different decomposition barriers and dissociation asymptotes. Although singlet and triplet [C2H6]2+ ions can exist as stable entities, they possess low energy barriers to decomposition. Vertical Franck-Condon transitions, involving electron impact ionization of ethane as well as charge-stripping collisions of [C2H6]+ ions, produce [C2H6]2+ ions which promptly dissociate since they are formed with energies in excess of various decomposition barriers. Appearance energies computed for doubly-charged ethane fragment ions are in accordance with experimental values.

Real-time evaluation of diffusion of the local anesthetic solution during peribulbar block using ultrasound imaging and clinical correlates of diffusion

The aims of this prospective observational study were to assess the incidence of intraconal spread during peribulbar (extraconal) anesthesia by real-time ultrasound imaging of the retro-orbital compartment and to determine whether a complete sensory and motor block (with akinesia) of the eye is directly related to the intraconal spread.

A Closed-Form Solution for the Optimal Time Evolution of an Exponentially Decaying Signal with Thermal Noise

The signal-to-noise ratio of a monoexponentially decaying signal exhibits a maximum at an evolution time of approximately 1.26 T-2. It has previously been thought that there is no closed-form solution to express this maximum. We report in this note that this maximum can be represented in a specific, analytical closed form in terms of the negative real branch of an inverse function known as the Lambert W function. The Lambert function is finding increasing use in the solution of problems in a variety of areas in the physical sciences. (C) 2014 Wiley Periodicals, Inc.

Characterization of the bovine IkappaB kinases (IKK)alpha and IKKbeta, the regulatory subunit NEMO and their substrate IkappaBalpha

The Nuclear factor (NF)-kappaB signalling pathway plays a critical role in the regulation and coordination of a wide range of cellular events such as cell growth, apoptosis and cell differentiation. Activation of the IKK (inhibitor of NF-kappaB kinase) complex is a crucial step and a point of convergence of all known NF-kappaB signalling pathways. To analyse bovine IKKalpha (IKK1), IKKbeta (IKK2) and IKKgamma (or NF-kappaB Essential MOdulator, NEMO) and their substrate IkappaBalpha (Inhibitor of NF-kappaB), the corresponding cDNAs of these molecules were isolated, sequenced and characterized. A comparison of the amino acid sequences with those of their orthologues in other species showed a very high degree of identity, suggesting that the IKK complex and its substrate IkappaBalpha are evolutionarily highly conserved components of the NF-kappaB pathway. Bovine IKKalpha and IKKbeta are related protein kinases showing 50% identity which is especially prominent in the kinase and leucine zipper domains. Co-immunoprecipitation assays and GST-pull-down experiments were carried out to determine the composition of bovine IKK complexes compared to that in human Jurkat T cells. Using these approaches, the presence of bovine IKK complexes harbouring IKKalpha, IKKbeta, NEMO and the interaction of IKK with its substrate IkappaBalpha could be demonstrated. Parallel experiments using human Jurkat T cells confirmed the high degree of conservation also at the level of protein-protein interactions. Finally, a yeast two-hybrid analysis showed that bovine NEMO molecules, in addition to the binding to IKKalpha and IKKbeta, also strongly interact with each other.

Impact of preservation solution on the extent of blood-air barrier damage and edema formation in experimental lung transplantation

A major aim in lung transplantation is to prevent the loss of structural integrity due to ischemia and reperfusion (I/R) injury. Preservation solutions protect the lung against I/R injury to a variable extent. We compared the influence of two extracellular-type preservation solutions (Perfadex, or PX, and Celsior, or CE) on the morphological alterations induced by I/R. Pigs were randomly assigned to sham (n = 4), PX (n = 5), or CE (n = 2) group. After flush perfusion with PX or CE, donor lungs were excised and stored for 27 hr at 4 degrees C. The left donor lung was implanted into the recipient, reperfused for 6 hr, and, afterward, prepared for light and electron microscopy. Intra-alveolar, septal, and peribronchovascular edema as well as the integrity of the blood-air barrier were determined stereologically. Intra-alveolar edema was more pronounced in CE (219.80 +/- 207.55 ml) than in PX (31.46 +/- 15.75 ml). Peribronchovascular (sham: 13.20 +/- 4.99 ml; PX: 15.57 +/- 5.53 ml; CE: 31.56 +/- 5.78 ml) and septal edema (thickness of alveolar septal interstitium, sham: 98 +/- 33 nm; PX: 84 +/- 8 nm; CE: 249 +/- 85 nm) were only found in CE. The blood-air barrier was similarly well preserved in sham and PX but showed larger areas of swollen and fragmented epithelium or endothelium in CE. The present study shows that Perfadex effectively prevents intra-alveolar, septal, and peribronchovascular edema formation as well as injury of the blood-air barrier during I/R. Celsior was not effective in preserving the lung from morphological I/R injury.

Human intestinal maltase-glucoamylase: crystal structure of the N-terminal catalytic subunit and basis of inhibition and substrate specificity

Human maltase-glucoamylase (MGAM) is one of the two enzymes responsible for catalyzing the last glucose-releasing step in starch digestion. MGAM is anchored to the small-intestinal brush-border epithelial cells and contains two homologous glycosyl hydrolase family 31 catalytic subunits: an N-terminal subunit (NtMGAM) found near the membrane-bound end and a C-terminal luminal subunit (CtMGAM). In this study, we report the crystal structure of the human NtMGAM subunit in its apo form (to 2.0 A) and in complex with acarbose (to 1.9 A). Structural analysis of the NtMGAM-acarbose complex reveals that acarbose is bound to the NtMGAM active site primarily through side-chain interactions with its acarvosine unit, and almost no interactions are made with its glycone rings. These observations, along with results from kinetic studies, suggest that the NtMGAM active site contains two primary sugar subsites and that NtMGAM and CtMGAM differ in their substrate specificities despite their structural relationship. Additional sequence analysis of the CtMGAM subunit suggests several features that could explain the higher affinity of the CtMGAM subunit for longer maltose oligosaccharides. The results provide a structural basis for the complementary roles of these glycosyl hydrolase family 31 subunits in the bioprocessing of complex starch structures into glucose.

Effects of Carnoy's solution on blood vessels of the axillary fossa of rats

Carnoy's solution is applied to reduce the recurrence of odontogenic keratocysts and unicystic ameloblastomas. The deleterious action of this fixative on nerves has been studied but no attention has been paid to its effects on nearby vessels. The aim of this study was to investigate the effects of Carnoy's solution on blood vessels. The rat axillary artery and vein were surgically exposed, soaked with Carnoy's solution and kept in place for 2, 5 or 10 min, depending on the treatment group. The 5-min group was followed for 1, 2 and 3 weeks postoperatively. The vessels in the 2-min and 5-min exposure groups showed histological changes to the vessels, represented by focal loss of the endothelium and hyalinization of the wall. These alterations increased in the 10-min group. The vessels in the 3-week observation period revealed signs of recovery. It is concluded that Carnoy's solution can damage blood vessels but the process is reversible for exposure times less than 5 min.

The Effect of the Fe2: Fe3 Ratio upon the Current Efficiency in the Electrolysis of a Copper Sulfate Solution Containing Iron Sulfate

In the treatment of copper ores by hydro-electro-metallurgical methods, not only is copper deposited, but other metals are also dissolved. In practice it has been found* that iron, under certain conditions, causes the copper to deposit on the cathode as a nonadherent precipitate and also that the iron in solution causes a great decrease in current efficiency, es­pecially when the electrolysis is conducted by operating with a higher current density at the cathode than at the anode. The present investigation deals with the effects of the two valences of iron on the current efficiency and endeavors to determine whether or not there is a ratio of the two at which point the efficiency becomes zero or approaches it.

Effect of Manganese and Arsenic upon Current Efficiency in the Deposition of Zinc from Zinc Sulphate Solution

Throughout the entire experiment the electrolysis were conducted in an eight-hundred cubic centimeter beaker. An excellent circulation of the solution was assured by means of an electric stirrer, vigorous gas evolution from the anodes, and by means of a regulated feed-discharge system. By means of this balance, solution of the same impurity concentration as that of the electrolyte was fed in the cell just as fast as the discharge was syphoned out.