Metric spaces with discrete topological fundamental group

With a certain natural topology, the fundamental group of a locally path connected metric space X becomes discrete if and only if X is semilocally simply connected. We include some related material and offer a counterexample to a similar result.     

Ueber die Hydratation und Erhärtung des Zementes

Ohne Zusammenfassung     

Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.

     

Stereoselective migration of sterically hindered organoboranes in cyclic and acyclic systems. A stereoselective allylic C-H activation reaction

The thermal migration of cyclic and acyclic organoboranes were studied. In most cases, a stereoselective 1,2-dyotropic migration was observed, allowing the stereocontrol of three contiguous chiral centers. Scope and limitations of this thermal migration are presented.     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

The diameter of randomly perturbed digraphs and some applications

The central observation of this paper is that if εn random arcs are added to any n‐node strongly connected digraph with bounded degree then the resulting graph has diameter 𝒪(lnn) with high probability. We apply this to smoothed analysis of algorithms and property testing. Smoothed Analysis: Recognizing strongly connected digraphs is a basic computational task in graph theory. Even for digraphs with bounded degree, it is NL‐complete. By XORing an arbitrary bounded degree digraph with a sparse random digraph R ∼ 𝔻_n,ε/n we obtain a “smoothed” instance. We show that, with high probability, a log‐space algorithm will correctly determine if a smoothed instance is strongly connected. We also show that if NL ⫅̸ almost‐L then no heuristic can recognize similarly perturbed instances of (s,t)‐connectivity. Property Testing: A digraph is called k‐linked if, for every choice of 2k distinct vertices s₁,…,s_k,t₁,…,t_k, the graph contains k vertex disjoint paths joining s_r to t_r for r = 1,…,k. Recognizing k‐linked digraphs is NP‐complete for k ≥ 2. We describe a polynomial time algorithm for bounded degree digraphs, which accepts k‐linked graphs with high probability, and rejects all graphs that are at least εn arcs away from being k‐linked. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Investigating laser rapid manufacturing for Inconel-625 components

This paper presents an investigation of laser rapid manufacturing (LRM) for Inconel-625 components. LRM is an upcoming rapid manufacturing technology, it is similar to laser cladding at process level with different end applications. In general, laser-cladding technique is used to deposit materials on the substrate either to improve the surface properties or to refurbish the worn out parts, while LRM is capable of near-net shaping the components by layer-by-layer deposition of the material directly from CAD model. In the present study, a high-power continuous wave (CW) CO₂ laser system, integrated with a co-axial powder-feeding system and a three-axis workstation were used. The effect of processing parameters during LRM of Inconel-625 was studied and the optimum set of parameters for the maximum deposition rate was established employing Orthogonal L9 array of Taguchi technique. Results indicated that the powder feed rate and the scan speed contributed about 56% and 26%, respectively to the deposition rate, while the influence of laser power was limited to 10% only. Fabricated components were subjected to non-destructive testing (like—ultrasonic testing, dye-penetrant testing), tensile testing, impact testing, metallographic examinations and micro-hardness measurement. The test results revealed defect-free material deposition with improved mechanical strength without sacrificing the ductility.