Analysis of hydrodynamic and thermal dispersion in porous media by means of a local approach

A pore scale analysis is implemented in this numerical study to investigate the behavior of microscopic inertia and thermal dispersion in a porous medium with a periodic structure. The macroscopic characteristics of the transport phenomena are evaluated with an averaging technique of the controlling variables at a pore scale level in an elementary cell of the porous structure. The Darcy–Forchheimer model describes the fluid motion through the porous medium while the continuity and Navier–Stokes equations are applied within the unit cell. An average energy equation is employed for the thermal part of the porous medium. The macroscopic pressure loss is computed in order to evaluate the dominant microscopic inertial effects. Local fluctuations of velocity and temperature at the pore scale are instrumental in the quantification of the thermal dispersion through the total effective thermal diffusivity. The numerical results demonstrate that microscopic inertia contributes significantly to the magnitude of the macroscopic pressure loss, in some instances with as much as 70%. Depending on the nature of the porous medium, the thermal dispersion may have a marked bearing on the heat transfer, particularly in the streamwise direction for a highly conducting fluid and certain values of the Peclet number.     

Cleavage of Diethyl Chromonyl α-Aminophosponate with Nitrogen and Carbon Nucleophiles: A Synthetic Approach and Biological Evaluations of a Series of Novel Azoles,Azines, and Azepines Containing α-Aminophosphonate and Phosphonate Groups

A convenient synthetic approach leading to a series of novel substituted azoles, azines, and azepines linked to the α-aminophosphonate moiety was achieved. The methodology depends on ring opening and ring closure (RORC) of the chromone ring of diethyl chromonyl α-aminophosphonate 1 via its reaction with nitrogen nucleophiles such as primary amines and 1,2-, 1,3-, and 1,4-bi-nucleophiles in ethanolic sodium ethoxide. Also, treatment of compound 1 with some acyclic and cyclic active methylene compounds under the same reaction conditions afforded interesting novel isolated and fused pyridine systems bearing phosphonate groups at the α-position. The screening of antimicrobial activity for the synthesized compounds indicates that connection of pyrazole, oxazepine, and benzodiazepine rings with α-aminophosphonate moiety exhibited good antimicrobial effects. Also, evaluation of their antioxidant properties shows that the compounds having 1,5-benzoxazepinyl and 1,5-benzodiazepinyl units in combination with α-aminophosphonic diester moiety are the most powerful antioxidant agents.     

Preparation and Reactions of 2‐Methyl‐7‐(3‐methyl‐5‐oxo‐1‐phenyl‐2‐pyrazolin‐4‐yl)‐5‐arylthiazolo[3,2‐a]‐pyrimido[4,5‐d]oxazin‐4(5H)‐one

Ethyl 7‐amino‐3‐(3‐methyl‐5‐oxo‐1‐phenyl‐2‐pyrazolin‐4‐yl)‐5‐aryl‐5H‐thiazolo[3,2‐a]pyrimidine‐6‐carboxylate was hydrolyzed with an ethanolic sodium hydroxide and the sodium salt thus formed underwent cyclization with acetic anhydride to afford 2‐methyl‐7‐(3‐methyl‐5‐oxo‐1‐phenyl‐2‐pyrazolin‐4‐yl)‐5‐arylthiazolo[3,2‐a]pyrimido[4,5‐d]oxazin‐4(5H)‐one. This compound was transformed to related heterocyclic systems via its reaction with various reagents. The biological activity of the prepared compounds was tested against Gram positive and Gram negative bacteria as well as yeast‐like and filamentous fungi. They revealed in some cases excellent biocidal properties.     

Combination of cysteine- and oligomerization domain-mediated protein immobilization on a surface plasmon resonance (SPR) gold chip surface

Here we report an effective method for protein immobilization on a surface plasmon resonance (SPR) gold chip, describing the combination of cysteine- and oligomerization domain-mediated immobilization of enhanced green fluorescent protein (EGFP) as a model protein for the purpose of orientation-controlled surface density packing. In order to facilitate the oligomerization of EGFP, the dimeric and trimeric constructs derived from GCN4- leucine zipper domain were chosen for multimeric EGFP assembly. For orientation-controlled immobilization of the protein, EGFP modified with cysteine residues showing excellent orientation on a gold chip was used as a starting protein, as previously reported in our earlier study (Anal. Chem., 2007, 79, 2680-2687). Constructs of EGFP with oligomerization domains were genetically engineered, and corresponding fusion proteins were purified, applied to a gold chip, and then analyzed under SPR. The immobilized EGFP density on a gold chip increased according to the states of protein oligomerization, as dimeric and trimeric EGFPs displayed better adsorption capability than monomeric and dimeric forms, respectively. Fluorescence measurement corroborated the SPR results. Taken together, our findings indicated that the combination of cysteine- and oligomerization domain-mediated immobilization of protein could be used in SPR biosensor applications, allowing for an excellent orientation and high surface density simultaneously.     

Some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity

The paper deals with some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity by direct variational method, Galerkin approach, and sub‐super solutions method. Our results are natural extension of Boulaaras' work in (Math Methods Appl Sci; 41(13):5203‐5210).     

Integral methods for computing solutions of a class of singular two-point boundary value problems

In this paper, we establish three iteration methods to compute solutions for a class of (weakly) singular two-point boundary value problems (xy^′)^′=f(x,y), where x(0,1) and <2. We obtain the sufficient conditions for existence of a unique solution on . Finally, we given some numerical examples.     

Analyse de complexité pour un théorème de Hall sur les fractions continues

We give a polynomial time controlled version of a theorem of M. Hall: every real number can be written as the sum of two irrational numbers whose developments into a continued fraction contain only 1, 2, 3 or 4. Mathematics Subject Classification: 03D15, 03F60, 11A55, 68Q25.     

Composite mix design in the production of asbestos/cement pipes

A mathematical model is presented for the determination of optimal mix of asbestos fibres to satisfy a set of desired pipe properties which vary with pipe size, class, and material availability. The approach utilizes a linear/separable programming model which is aimed at minimizing the total cost of fibres used. The fibre properties, such as reinforcing strength, processability, and length as well as cost and stocks available are taken into account in the model. Also represented are the profile of the ideal mix relative to the required composite strength, processability, and ‘dust content’. Asbestos mixes designed using the model have been implemented in the production of asbestos/cement pipes in one of the asbestos/cement pipe manufacturing plants in the Gulf area. Optimum model mixes have demonstrated significant technical and economic merits over the conventionally designed mixes.