Phase-shift, refraction and focusing based on the metamaterial technologies

We address the problem of positive phase-shifting, negative refraction and focusing via a flat lens on the basis of the metamaterial technologies. With this aim, three examples are considered which differ by the technology employed and the operating frequency. The first one concerns negative-zero-positive refraction by using a prism-shaped electromagnetic metamaterial which consists of omega-type inclusion arrays operating at microwaves. The experimental verification was done in this case by angle-resolved transmission measurements. Second, we report on the phase-shift properties of a negative index transmission line which operates at Terahertz frequencies. In order to experimentally demonstrate the left-handed character of the propagation along the line, resulting in a phase advance, we used time domain experiments. At last, focusing by double refraction in a flat negative index lens was demonstrated by the theoretical and experimental mapping of the intensity of the electric field. Such a mapping of the E-field was carried out at near infrared (1.5 μm) by analysis in the time domain and scanning by near field optical microscopy. To cite this article: D. Lippens, C. R. Physique 10 (2009).     

Limiting conditions for compression testing of flat specimens in the split hopkinson pressure bar

The split Hopkinson pressure bar (SHPB) technique is analyzed during the initial stages of loading by means of axisymmetric finite element simulations of dynamic compression tests. Limiting strains as functions of the test parameters such as the specimen diameterd and heighth were found to ensure a one-dimensional stress state and axial stress homogeneity in specimens of elastic-perfectly plastic material. The one-dimensional stress state is necessary and sufficient for accurate test results for flat specimens (h/d≤0.5) and nonflat specimens, respectively, with diameters up to half of the bar diameter. Only very small values of the Coulomb friction constraint (μ≈0.01) seem to be acceptable. The significance of the determined limiting conditions to the more practical case of a rate dependent material is investigated using an elastic-viscoplastic material for the specimen. The stress and strain rate reconstructed from the calculated bar signals (according to the SHPB analysis) are compared with stresses and strain rates averaged over the cross section of the specimen. Well-known inertia corrections improve the results of the SHPB procedure, but errors remain for small strains and highly time dependent strain rates.     

The toughness of split graphs

In this short note we argue that the toughness of split graphs can be computed in polynomial time. This solves an open problem from a recent paper by Kratsch et al. (Discrete Math. 150 (1996) 231–245).     

Application of the “cooled needle” technique to split and splitless sampling onto capillary columns

Cooled needle sampling using syringes was applied to splitless injection and to simulated distillation analyses. Slight changes of the construction of the previous device are also described. The changes concern the temperature profile within the injector and especially the vaporization insert. Even with the low carrier gas flow through the injector during splitless injection, discrimination by component volatility can be avoided. Precision and accuracy of simulated distillation data obtained with split sampling also can be improved by the cooled needle technique.     

Splitting tendency of cellulosic fibers – Part 1. The effect of shear force on mechanical stability of swollen lyocell fibers

A procedure for splitting of a lyocell fiber into a multitude of finer fibrils was developed. Crockmeter, usually used for rub-fastness of colored textiles, was modified and used for obtaining required shear force on swollen lyocell fiber. The shear force applied on fibers, and the concentration of NaOH, which affects swelling degree of fiber, were shown to be the leading parameters determining split number of lyocell fiber. While number of shear cycles was found to be of minor relevance for fiber splitting, the applied pressure directly influences the number of splitted fibrils. For example, at a pressure of 34.8 kPa, the average split number of lyocell fiber in 2.5 M NaOH solution was observed as 15, whereas it was observed as 30 for 47 kPa and 41 for 59.3 kPa. Splitting was not observed above 5 M of NaOH solution. Analyses of fiber splitting permit new aspects to study inner structure of lyocell.     

Glass wool in the inserts of split injectors for capillary GC?

It has been reported that glass wool packed tightly into the glass liner of a vaporizing injector used in the splitting mode considerably reduces the standard deviation of the results obtained, because of improved evaporation of the sample prior to reaching the split point at the capillary column entrance. This finding could not be reproduced on using the same sample composition as reported in the literature, i.e. methanol/2-ethyl-1-hexanol (1:1). The standard deviations obtained were between 3 and 10% (depending on the conditions selected) and were not influenced significantly by the introduction of glass wool. The peak area ratio (methanol/2-ethyl-1-hexanol) was found to depend on a number of parameters, such as: injector temperature; glass liner internal diameter; syringe handling technique; the relative position of the syringe needle exit and capillary column entrance; the sample volume injected; and the packing of the glass liner. Generally, the area ratio deviated further from the correct one (determined by cold on-column sampling) when the glass liner was packed with glass wool. On the basis of the results, it is speculated that either a complete evaporation of the sample should be achieved (which appears to be impossible under the conditions we used) or, alternatively, the sample should be given the least possible opportunity to evaporate, thus allowing it to enter the column in the form of droplets. The results were worse in terms of precision and accuracy the greater the partition of sample components between the liquid (droplet) and vapor phase. It is concluded that the use of evaporation aids such as glass wool cannot be generally recommended.     

Characterizations of Levitin–Polyak well-posedness by perturbations for the split variational inequality problem

The purpose of this paper is to investigate Levitin–polyak well-posedness by perturbations of the split variational inequality problem in reflexive Banach spaces. Furi-Vignoli-type characterizations are established for the well-posedness. We prove that the weak generalized Levitin–Polyak well-posedness by perturbations is equivalent to the nonemptiness and boundedness of the solution set of the problem. Finally, we discuss the relations between the Levitin–Polyak well-posedness by perturbations of the split variational inequality problem and the Levitin–Polyak well-posedness by perturbations of the split minimization problem when the split variational inequality problem arises from the split minimization problem.     

Chromatic capacity and graph operations

The chromatic capacityχ_cap(G) of a graph G is the largest k for which there exists a k-coloring of the edges of G such that, for every coloring of the vertices of G with the same colors, some edge is colored the same as both its vertices. We prove that there is an unbounded function f:N→N such that χ_cap(G)?f(χ(G)) for almost every graph G, where χ denotes the chromatic number. We show that for any positive integers n and k with k?n/2 there exists a graph G with χ(G)=n and χ_cap(G)=n-k, extending a result of Greene. We obtain bounds on that are tight as r→∞, where is the complete n-partite graph with r vertices in each part. Finally, for any positive integers p and q we construct a graph G with χ_cap(G)+1=χ(G)=p that contains no odd cycles of length less than q.