ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Two Dimensional Numerical Simulation of Highly-Strained Hydrogen-Air Opposed Jet Laminar Diffusion Flames

In this study, a detailed 2-D numerical technique is utilized to investigate the structure, and flame extinction and restoration characteristics of laminar hydrogen-air opposed jet diffusion flames, using both plug (uniform) and parabolic inflow boundary conditions for 3 millimeter jet tubes, spaced 6 millimeters apart and imbedded in low velocity coflows. First, by using the most recent of two chemical kinetic models, excellent agreement was obtained between calculated distributions of temperature and major species, and published UV laser Raman scattering measurements, for 50% and 100% hydrogen-air flames over a range of input strain rates. Agreement with measured OH profiles was reasonably good at high strain rates, but generally less so at low strain rates. Also, the numerically simulated extinction limit of the 100% hydrogen-air diffusion flame was predicted within −5.1% (Jachimowski kinetic model) and +4.7% (Yetter et. al model) of a published grand-average measurement of global applied stress on the airside (average input velocity/tube-diameter), obtained using parabolic inflow profiles with a 2.7 millimeter tube opposed jet burner system. Second, the study showed counterflow flame extinction limits for 100% hydrogen-air were most consistent when compared using flame core maximum radial strain rates on the center-line. By this measure, flame extinction occurred at similar strain rates (within 9.6%) for the two very different inflow boundary types. Also, the respective radial strain rates were linearly proportional to both centerline maximum axial strain rate and global applied stress rate, up to and just before the extinction state. Thus, both of these measurable reference rates provided a suitable relative basis for characterizing flame extinction limits. However, the ratio of radial to axial strain rates varied significantly with input flow boundary types. The plug input flame resulted in a slightly smaller (0.92×) radial flame core strain rate on the centerline than the maximum axial strain rate, and this measure can be compared to the parabolic inflow flame which had a relatively larger (1.47×) radial strain rate. Furthermore, the respective radial/axial ratios (0.92 and 1.47) were not even close to the “classic” 0.50 ratio for the near-extinction state derived from the simplest 1-D stream-function approximation (Heimentz or potential flow) method. Finally, a previously observed ring-shaped post-extinction 100% hydrogen-air flame was numerically simulated when the stretching limit of the parabolic input velocity (for a 3 millimeter opposed jet) was exceeded beyond the critical extinction point. The post-extinction flame was tri-brachial, with fuel-rich and fuel-lean diffusion and premixed branches, displaying a quite different flame structure than the typical counterflow diffusion flame

Alcune note sulle funzioni di seminorma frazionaria Ws,1 minima

In this survey we discuss some existence and asymptotic results, originally obtained in [4,3], for functions of least Ws,1-fractional seminorm. We present the connection between these functions and nonlocal minimal surfaces, leveraging this relation to build a function of least fractional seminorm. We further prove that a function of least fractional seminorm is the limit for p → 1 of the sequence of minimizers of the Ws,p-energy. Additionally, we consider the fractional 1-Laplace operator and study the equivalence between weak solutions and functions of least fractional seminorm.In questa nota discutiamo alcuni risultati di esistenza e asintotici, originariamente ottenuti in [4,3], per le funzioni di seminorma frazionaria Ws,1 minima. Presentiamo la connessione tra queste funzioni e le superfici minime nonlocali, e ricorriamo a tale relazione per costruire una funzione di seminorma frazionaria minima. Otteniamo inoltre una funzione di seminorma frazionario minima come limite per p → 1 del minimo dell'energia frazionaria Ws,p. Consideriamo in più l'1-Laplaciano frazionario e mostriamo l'equivalenza tra le soluzioni deboli e le funzioni di seminorma frazionaria Ws,1 minima

Effect of nutritional factors on the growth and production of biosurfactant by Pseudomonas aeruginosa strain 181

The growth and production of biosurfactant by P. seudomonas aeruginosa (181) was dependant on nutritional factors. Among the eleven carbon sources tested, glucose supported the maximum growth (0.25 g/L) with the highest biosurfactant yield and this was followed by glycerol. Glucose reduced the surface tension to 35.3 dyne/ cm and gave an E24 reading of 62.7%. Butanol gave the lowest growth and had no biosurfactant production. For the nitrogen sources tested, casamino acid supported a growth of 0.21 g/L which reduced the surface tension to 41.1 dyne/cm and gave an E24 reading of 56%. Soytone was assimilated similarly, with good growth and high biosurfactant production. Corn steep liquor gave the lowest growth and did not show any biosurfactant activity

Efficient approximation of functions of some large matrices by partial fraction expansions

Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$ is a vector, are based on partial fraction expansions. However, some of these techniques require solving several linear systems whose matrices differ from $A$ by a complex multiple of the identity matrix $I$ for computing $\Psi(A)\mathbf{v}$ or require inverting sequences of matrices with the same characteristics for computing $\Psi(A)$. Here we study the use and the convergence of a recent technique for generating sequences of incomplete factorizations of matrices in order to face with both these issues. The solution of the sequences of linear systems and approximate matrix inversions above can be computed efficiently provided that $A^{-1}$ shows certain decay properties. These strategies have good parallel potentialities. Our claims are confirmed by numerical tests