An exact solution for one-dimensional unsteady nonlinear groundwater flow

After a brief review of the validity of Darcy's law, a nonlinear flow law is adopted for the analytical solution of a groundwater flow problem. A one-dimensional unsteady flow in plane geometry, with prescribed head at the boundaries, is studies. The solution of the analogous linear case is reviewed through the use of Boltzmann's transformation. A solution for nonlinear flow is obtained through a generalization of this transformation. Detailed expressions for specific discharge and drawdown are derived for two significant values of the exponent of the flow law. All results are presented in dimensionless form for a comparative analysis. Some significant cases are plotted. Finally, some implications of the adoption of a nonlinear flow law are discussed.

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Sommario Dopo un breve riepilogo sui limiti di validità della legge di Darcy, si adotta una formulazione non lineare della legge del moto per la risoluzione analitica di un problema di filtrazione. Si studia un moto non stazionario monodimensionale in geometria piana, con carico assegnato al contorno. Viene richiamata la soluzione dell'analogo caso lineare, tramite l'applicazione della trasformata di Boltzmann. Una soluzione per il moto non lineare è ottenuta mediante la generalizzazione di tale trasformazione. Si ricavano le espressioni della velocità apparente di filtrazione e del drawdown per due valori significativi dell'esponente della legge del moto. Tutti i risultati sono presentati in forma adimensionale per una analisi comparativa. Alcuni casi significativi sono diagrammati. In conclusione, sono discusse alcune implicazioni dell'adozione di una legge del moto non lineare.

     

Homology computation for a class of contact structures on T^3

We consider a family of tight contact forms on the three-dimensional torus and we compute the relative Contact Homology by using the variational theory of critical points at infinity. We will also show local stability.     

4‐[4‐(Di­methyl­amino)­benzyl­idene­amino]‐3,5‐bis(2‐pyridyl)‐4H‐1,2,4‐triazole

The title compound, C₂₁H₁₉N₇, is a poly­pyridine ligand that is suitable for assembling complex metal systems capable of photoinduced electron transfer. The solid‐state structure has been determined at room temperature by single‐crystal X‐ray diffraction. The mol­ecule is not flat and both the bis­(pyridyl)­triazole and the benzyl­id­ene­amine fragments show significant distortions from planarity.     

Electrophilicity Scale of Activated Amides: 17O NMR and 15N NMR Chemical Shifts of Acyclic Twisted Amides in N−C(O) Cross-Coupling

The structure and properties of amides are of tremendous interest in organic synthesis and biochemistry. Traditional amides are planar and the carbonyl group non-electrophilic due to n_N→π*_C=O conjugation. In this study, we report electrophilicity scale by exploiting ¹⁷O NMR and ¹⁵N NMR chemical shifts of acyclic twisted and destabilized acyclic amides that have recently received major attention as precursors in N-C(O) cross-coupling by selective oxidative addition as well as precursors in electrophilic activation of N-C(O) bonds. Most crucially, we demonstrate that acyclic twisted amides feature electrophilicity of the carbonyl group that ranges between that of acid anhydrides and acid chlorides. Furthermore, a wide range of electrophilic amides is possible with gradually varying carbonyl electrophilicity by steric and electronic tuning of amide bond properties. Overall, the study quantifies for the first time that steric and electronic destabilization of the amide bond in common acyclic amides renders the amide bond as electrophilic as acid anhydrides and chlorides. These findings should have major implications on the fundamental properties of amide bonds.     

Microcalorimetry of O2 and NO on flat and stepped platinum surfaces

Using the single-crystal adsorption calorimeter (SCAC), coverage-dependent heats of adsorption and sticking probabilities are reported for O₂ and NO on Pt{1 1 1}, Pt{2 1 1} and Pt{4 1 1} at 300 K. At low coverage, oxygen adsorption is dissociative for all Pt surfaces. The highest initial heat of adsorption is found on Pt{2 1 1}, with a value of 370 kJ/mol, followed by those on Pt{4 1 1} (310 kJ/mol) and Pt{1 1 1} (300 kJ/mol). We attribute this relatively large difference in the dissociative heat of adsorption at low coverage to the step character of the {2 1 1} surface. Initial sticking probabilities, s_o, are similar for the three surfaces, 0.22 on Pt{1 1 1}, 0.17 on Pt{2 1 1} and 0.18 on Pt{4 1 1}, rapidly decreasing as the oxygen coverage increases. For nitric oxide, the initial heats of adsorption are very similar and consistent with either dissociative or molecular adsorption, with values of 182 kJ/mol on Pt{1 1 1}, 192 kJ/mol on Pt{2 1 1} and 217 kJ/mol on Pt{4 1 1}. The s_o value is virtually identical for all three systems, with values ranging from 0.82 to 0.85, suggesting that the initial sticking probability is insensitive to the surface structure and adsorption is intrinsically precursor mediated. SCAC data are also used to evaluate pre-exponential factors, ν, for first-order desorption at high coverage where adsorption is non-dissociative. Values of 3 × 10¹⁸, 6 × 10¹⁸ and 2 × 10¹⁸ s^?1 for O₂, and 4 × 10¹⁹, 6 × 10¹⁷ and 2 × 10²⁰ s^?1 for NO on Pt{1 1 1}, Pt{2 1 1} and Pt{4 1 1}, respectively, are found. These unexpectedly high values are rationalised in terms of conventional transition state theory entropy changes.     

Benders decomposition, Lagrangean relaxation and metaheuristic design

Large part of combinatorial optimization research has been devoted to the study of exact methods leading to a number of very diversified solution approaches. Some of those older frameworks can now be revisited in a metaheuristic perspective, as they are quite general frameworks for dealing with optimization problems. In this work, we propose to investigate the possibility of reinterpreting decompositions, with special emphasis on the related Benders and Lagrangean relaxation techniques. We show how these techniques, whose heuristic effectiveness is already testified by a wide literature, can be framed as a “master process that guides and modifies the operations of subordinate heuristics”, i.e., as metaheuristics. Obvious advantages arise from these approaches, first of all the runtime evolution of both upper and lower bounds to the optimal solution cost, thus yielding both a high-quality heuristic solution and a runtime quality certificate of that same solution.     

Testing the structure of multistage stochastic programs

A fixed topology of stages and/or a fixed branching scheme are common assumptions for applications and numerical solution of scenario based multistage stochastic programs. Using contamination technique to test this structure, we extend the results of Dupačová (Contamination for multistage stochastic programs. In: Hušková M, Janžura M (eds) Prague stochastics. Matfyzpress, Praha, pp 91–101, 2006a) to stochastic programs with multistage polyhedral risk objectives. The ideas are exemplified by bond portfolio management problems and complemented by illustrative numerical results.     

The extracellular matrix of the human aortic wall: ultrastructural observations by FEG-SEM and by tapping-mode AFM

Fragments of human ascending aorta harvested during heart surgery were cryofractured and observed by scanning electron microscopy (SEM) and atomic force microscopy (AFM). Elastic fibers appear as irregular, undulated laminae of variable size and shape. Their surface shows an evident fibrous texture suggestive of a criss-crossed, delicate filamentous scaffold and is marked by a number of features such as ridges, holes and protruding ribs. At higher magnification, both SEM and AFM show the surface composed of a finely granular material, with a bead size of approximately 20 nm. However, the thickness of the metal coating in one case, and the tip convolution effect on the other, may equally result in an artifactual enlargement of the structures, so that the beads may be significantly smaller. The surfaces created by the fracture always appear smooth and compact and with this technique do not reveal significant detail. The collagen component is mostly represented by small, uniform fibrils gathered in flexuous bundles and following a wavy course not unlike that of the elastic laminae. An orthogonal lattice of small proteoglycans is readily evident even without a specific treatment. Occasionally, the fibrils appear encrusted or engulfed in a grainy matrix reminiscent of the elastic fiber surface. Fluid Tapping-Mode Atomic Force Microscopy simultaneously reveals the surface-bound proteoglycans and the inner architecture of the fibrils, composed of smaller subunits following a spiral course with a winding angle of approximately 17 degrees.