One-Parameter Fixed-Point Theory and Gradient Flows of Closed 1-Forms

We use the one-parameter fixed-point theory of Geoghegan and Nicas to get information about the closed orbit structure of transverse gradient flows of closed 1-forms on a closed manifold M. We define a noncommutative zeta function in an object related to the first Hochschild homology group of the Novikov ring associated to the 1-form and relate it to the torsion of a natural chain homotopy equivalence between the Novikov complex and a completed simplicial chain complex of the universal cover of M.     

Observation of hydrogen induced intermediate borides in PrFeB based alloys by Mössbauer effect spectroscopy

In the present work, a quantitative analysis of the phase compositions by Mössbauer effect spectroscopy of solid and conventional hydrogen disproportionated Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys was carried out. Significant amounts of intermediate borides t-Fe₃B and Pr(Fe, Co)₁₂B₆ were detected after solid hydrogen disproportionation treatment in Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys, respectively. After conventional hydrogenation–disproportionation–desorption–recombination treatment these phases were not detected and in no case residual Pr₂Fe₁₄B-phase was found. It was observed that the amount of intermediate borides after disproportionation can be correlated with the degree of texture after recombination at various temperatures.     

Pressure effects on the quadrupole coupling constant of 7Li in first stage lithium graphite

The pressure dependence of the experimental ⁷Li NMR spectra is reported for first stage lithium graphite (LiC₆) intercalation compound at temperatures T = 232 and 293 K. This experiment together with the presented point charge model calculation of the ⁷Li quadrupole coupling constant $\text{(}\text{e}{}^2\text{qQ}\text{h}\text{)}$ allows an unambiguous determination of the sign of e²qQ/h which is negative: $\text{e}{}^2\text{qQ}\text{h=-52 kHz}$ at p = 1 bar and T = 232 K. The averaged location of the electrons transferred from the Li intercalant to the graphite layers, as estimated in this study, is in excellent agreement with earlier theoretical energy-band calculations. The compressibility of LiC₆ in the c-direction is predicted to be k_c = 1.7 × 10^-12cm²dyn^-1, it agrees with estimates derived from the available phonon dispersion relations.     

Iterative solutions for low lying excited states of a class of SchrSdinger equation

The convergent iterative procedure for solving the groundstate Schr?dinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.     

A new technique for fluid velocimetry based on near field scattering

We show that the time evolution of near-field scattering speckles, originated by a fluid suspension of particles, provides information about the velocity field in the fluid. This information can be extracted from a statistical analysis of speckle fields taken at different times, either by measuring their cross-correlation function or by recovering the power spectrum corresponding to the difference between the two speckle fields. Experimental data are in accordance to the expected behaviors. The results are independent of the scatterer's size, allowing one to exploit the technique also with sub-wavelength tracking particles.     

Efficient domain partitioning algorithms for global optimization of rational and Lipschitz continuous functions

A domain partitioning algorithm for minimizing or maximizing a Lipschitz continuous function is enhanced to yield two new, more efficient algorithms. The use of interval arithmetic in the case of rational functions and the estimates of Lipschitz constants valid in subsets of the domain in the case of others and the addition of local optimization have resulted in an algorithm which, in tests on standard functions, performs well.     

Local search algorithms for the min-max loop layout problem

In the min-max loop layout problem, machines are to be arranged around a loop of conveyor belt. The ordering of the machines dictates the number of circuits of the conveyor belt required to manufacture each of several products. The goal is to find an ordering of the machines that minimises the maximum number of circuits required for the manufacture of any of the products. Since the problem is strongly NP-hard, the study of heuristic methods is of interest. This paper proposes iterated descent and tabu search algorithms, and a randomised insertion algorithm. Results of extensive computational tests show that all of our algorithms outperform a previously known algorithm that applies a greedy heuristic to the solution of a linear programming relaxation. The best quality solutions are obtained with iterated descent. This adds further evidence to the belief that iterated descent can produce high quality solutions to a variety of combinatorial optimisation problems. Moreover, unlike some other local search algorithms, iterated descent does not require much tuning in order to be competitive.