Automata and logics over finitely varying functions

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called View the MathML source’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich (2002) [15]. We also identify a “counter-free” subclass of View the MathML source’s which characterise the first-order definable languages of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic (MTL) Chevalier et al. (2006, 2007) [6] and [7].

Counter-free input-determined timed automata

We identify a class of timed automata, which we call counter-free input-determined automata, which characterize the class of timed languages definable by several timed temporal logics in the literature, including MTL. We make use of this characterization to show that MTL+Past satisfies an “ultimate stability” property with respect to periodic sequences of timed words. Our results hold for both the pointwise and continuous semantics. Along the way we generalize the result of McNaughton-Papert to show a counter-free automata characterization of FO-definable finitely varying functions.

On continuous timed automata with input-determined guards

We consider a general class of timed automata parameterized by a set of “input-determined” operators, in a continuous time setting. We show that for any such set of operators, we have a monadic second order logic characterization of the class of timed languages accepted by the corresponding class of automata. Further, we consider natural timed temporal logics based on these operators, and show that they are expressively equivalent to the first-order fragment of the corresponding MSO logics. As a corollary of these general results we obtain an expressive completeness result for the continuous version of MTL.

Structural, thermal, and electrical properties of CrSi2

Stoichiometric CrSi2 was prepared by arc melting and compacted by uniaxial hot pressing for property measurements. The crystal structure of CrSi2 was investigated using the powder x-ray diffraction method. From the Rietveld refinement, the lattice parameters were found to be a = 4.427 57 (7) and c = 6.368 04 (11) Å, respectively. The thermal expansion measurement revealed an anisotropic expansion in the temperature range from room temperature 800 K with αa = 14.58×10−6/K, αc = 7.51×10−6/K, and αV = 12.05×10−6/K. The volumetric thermal expansion coefficient shows an anomalous decrease in the temperature range of 450–600 K. The measured electrical resistivity ρ and thermoelectric power S have similar trends with a maxima around 550 K. Thermal conductivity measurements show a monotonic decrease with increasing temperature from a room temperature value of 10 W m−1 K−1. The ZT values increase with temperature and have a maximum value of 0.18 in the temperature range studied. An analysis of the electronic band structure is provided.

Diffusion mechanism in XSi2 and X5Si3 (X= Nb, Mo, V) phases

In view of the importance of the suicides in the high temperature applications, the diffusion behaviour is compared in different systems for two types of silicides, XSi2 and X5Si3 (X=Nb, Mo, V). Atomic mechanism of diffusion and defects present in the structure are discussed. In both the phases, Si has faster diffusion rate than the metal species. This is expected from the nearest neighbour (NN) bonds present in the XSi2 phase but rather unusual in the X5Si3 phase. Relative mobilities of the species calculated indicate the presence of high concentration of Si antisites. Moreover, the concentration of the defects is different in different systems to find different diffusion rates.

Interdiffusion in Nb-Mo, Nb-Ti and Nb-Zr systems

Diffusion couple technique is used to study interdiffusion in Nb-Mo, Nb-Ti and Nb-Zr systems. Interdiffusion coefficients at different temperatures and compositions are determined using the relation developed by Wagner. The change in activation energy for interdiffusion with composition is determined. Further, impurity diffusion coefficient of the species are determined and compared with the available data in literature.

Diffusion mechanism in the mu phase in Nb-X (X = Ni, Co, Fe) systems

Nb is one of the common refractory elements added in Ni, Co and Fe based superalloys. This lead to the formation of brittle topological close packed (tcp) mu phase, which is deleterious to the structure. It mainly grows by interdiffusion and in the present article, the interdiffusion process in different Nb-X (X=Ni, Co, Fe) systems is discussed. The activation energy for interdiffusion is lower in the Co-Nb system (173 kJ/mol) than Fe-Nb system (233 kJ/mol), which is again lower than the value found in the Ni-Nb system (319.7 kJ/mol). The mole fraction of Nb in this phase is less than Fe or Co at stoichiometric compositions in the Nb-Fe (that is Fe7Nb6) and Nb-Co (that is Co7Nb6) systems. On the other hand, the mole fraction of Nb is higher than Ni in the same phase (Ni6Nb2) in Ni-Nb system. However, in all the phases, Nb has lower diffusion rate. Possible diffusion mechanism in this phase is discussed with respect to the crystal structure.

Effect of co-substitution of Mn and Al on thermoelectric properties of chromium disilicide

CrSi2 was earlier reported to be an interesting thermoelectric material for high temperature applications because of its high oxidation resistance and good mechanical properties. In order to enhance its figure of merit, Mn at Cr site and Al at Si site were substituted into CrSi2. Our results indicate that Cr1-x Mn (x) Si2-x Al (x) solid solutions exhibit significantly lower thermal conductivity and a higher figure of merit than CrSi2.

Thermoelectric properties of chromium disilicide prepared by mechanical alloying

CrSi and Cr1-x Fe (x) Si particles embedded in a CrSi2 matrix have been prepared by hot pressing from CrSi1.9, CrSi2, and CrSi2.1 powders produced by ball milling using either WC or stainless steel milling media. The samples were characterized by powder X-ray diffraction, scanning, and transmission electron microscopy and electron microprobe analysis. The final crystallite size of CrSi2 obtained from the XRD patterns is about 40 and 80 nm for SS- and WC-milled powders, respectively, whereas the size of the second phase inclusions in the hot pressed samples is about 1-5 mu m. The temperature dependence of the electrical resistivity, Seebeck coefficient, thermal conductivity, and figure of merit (ZT) were analyzed in the temperature range from 300 to 800 K. While the ball-milling process results in a lower electrical resistivity and thermal conductivity due to the presence of the inclusions and the refinement of the matrix microstructure, respectively, the Seebeck coefficient is negatively affected by the formation of the inclusions which leads to a modest improvement of ZT.