Critical exponents in the transition to chaos in one-dimensional discrete systems

We report the numerically evaluated critical exponents associated with the scaling of generalized fractal dimensions during the transition from order to chaos. The analysis is carried out in detail in the context of unimodal and bimodal maps representing typical one-dimensional discrete dynamical systems. The behavior of Lyapunov exponents (LE) in the cross over region is also studied for a complete characterization.     

K-causal structure of space-time in general relativity

Using K-causal relation introduced by Sorkin and Woolgar [1], we generalize results of Garcia-Parrado and Senovilla [2,3] on causal maps. We also introduce causality conditions with respect to K-causality which are analogous to those in classical causality theory and prove their inter-relationships. We introduce a new causality condition following the work of Bombelli and Noldus [4] and show that this condition lies in between global hyperbolicity and causal simplicity. This approach is simpler and more general as compared to traditional causal approach [5,6] and it has been used by Penrose et al [7] in giving a new proof of positivity of mass theorem. C ⁰-space-time structures arise in many mathematical and physical situations like conical singularities, discontinuous matter distributions, phenomena of topology-change in quantum field theory etc.      

Effect of image fiber on the speckle fringe pattern in image fiber-guided DSPI endoscopy

The effect of using an image fiber on the speckle fringe visibility in an endoscopic DSPI is analyzed here. An endoscope system was designed and developed, using image fiber as the speckle pattern image conduit, to work in the out-of-plane speckle interferometric configuration and experiments were carried out using a curved phantom tissue specimen as the test target. Experimental results obtained using the developed system are compared with that obtained using conventional DSPI system. To obtain a relative and quantitative comparison of the quality of the fringes obtained employing the two methods, an evaluation method that can give a quantified ‘score’ is proposed here.     

A new polymorph of FeAlO3 at high pressure

Synchrotron X-ray diffraction measurements confirmed that a new polymorph of FeAlO3 could be synthesized at about 1800 K and 72 GPa. This phase can be indexed on an orthorhombic cell and transforms into the trigonal form on release of pressure. The c/a ratio of about 2.71 of the trigonal phase suggests corundum structure of FeAlO3 rather than LiNbO3 or ilmenite structure. This conclusion also suggests that the high-pressure orthorhombic phase could be the Rh2O3(II) structure rather than the GdFeO3-type perovskite structure.     

Electrical conductivity and dielectric relaxation studies on microwave synthesized Na<Subscript>2</Subscript>SO<Subscript>4</Subscript>·NaPO<Subscript>3</Subscript>·MoO<Subscript>3</Subscript> glasses

Electrical conductivity and dielectric relaxation studies on SO₄ ^2? doped modified molybdo-phosphate glasses have been carried out over a wide range of composition, temperature and frequency. The d.c. conductivities which have been measured by both digital electrometer (four-probe method) and impedance analyser are comparable. The relaxation phenomenon has been rationalized using electrical modulus formalism. The use of modulus representation in dielectric relaxation studies has inherent advantages viz., experimental errors arising from the contributions of electrode-electrolyte interface capacitances are minimized. The relaxation observed in the present study is non-Debye type. The activation energies for relaxation were determined using imaginary parts of electrical modulus peaks which were close to those of the d.c. conductivity implying the involvement of similar energy barriers in both the processes. The enhanced conductivity in these glasses can be attributed to the migration of Na⁺, in expanded structures due to the introduction of SO₄ ^2? ions.     

Mixed-ligand chelate extraction of trivalent lanthanides with 4,4,4-trifluoro-1-phenyl-1,3-butanedione and neutral oxo-donors

Mixed-ligand chelate extraction of trivalent lanthanides such as Nd(III), Eu(III) and Lu(III) into benzene with mixtures of 4,4,4-trifluoro-1-phenyl-1,3-butanedione (HBFA) and bis-2-ethylhexyl sulphoxide (B2EHSO) or triphenylphosphine oxide (TPhPO) from thiocyanate solutions was investigated. The results demonstrate that these metal ions are extracted as Ln(BFA)(3) with HBFA alone and in the presence of a neutral oxo-donor, B2EHSO or TPhPO(S), as Ln(BFA)(3).S and Ln(BFA)(3).2S. The equilibrium constants of the above species increase monotonically with decreasing ionic radii of these metals ions. The addition of a neutral donor to the metal chelate system not only enhances the extraction efficiency but also improves the selectivity among these trivalent lanthanides. Hence this mixed-ligand system may be useful for the extraction and separation of individual lanthanides and also for the separation of lanthanides as a group from other metal ions.     

Effect of water soluble complexing agent on the extraction of Ce(III) and Nd(III) by 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester

Extraction of Ce(III) and Nd(III) by 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (EHEHPA) in the presence of water soluble complexing agent, glycine, has been studied. An improvement in separation factor between these lanthanides is observed. The extraction data have been analyzed theoretically, taking into account complexation of the metal in the aqueous phase with glycine and chloride ion and plausible complexation in the organic phase.     

Surface Modification on Nickel Rich Cathode Materials for Lithium-Ion Cells: A Mini Review

Nickel-rich (Ni-rich) layered oxides are considered as the most promising cathode candidates for lithium-ion cells owing to their high theoretical specific capacity. However, the higher nickel content endows structural deformation through unwanted phase transitions and parasitic side reactions that lead to capacity fading upon prolonged cycling. Hence, a deep understanding of the chemistry and structural behaviour is essential for developing Ni-rich Lithium Nickel Cobalt Manganese oxide (NCM) cathode-based high-energy batteries. The present review focuses on the different challenges associated with Ni-rich NCM materials and surface modification as a strategy to solve the issues associated with NCM materials, assessment of several coating materials, and the recent developments in the surface modification of Ni-rich NCMs, with an in-depth discussion on the impact of coating on the degradation mechanism.     

Stationary,completely mixed and symmetric optimal and equilibrium strategies in stochastic games

In this paper, we address various types of two-person stochastic games—both zero-sum and nonzero-sum, discounted and undiscounted. In particular, we address different aspects of stochastic games, namely: (1) When is a two-person stochastic game completely mixed? (2) Can we identify classes of undiscounted zero-sum stochastic games that have stationary optimal strategies? (3) When does a two-person stochastic game possess symmetric optimal/equilibrium strategies? Firstly, we provide some necessary and some sufficient conditions under which certain classes of discounted and undiscounted stochastic games are completely mixed. In particular, we show that, if a discounted zero-sum switching control stochastic game with symmetric payoff matrices has a completely mixed stationary optimal strategy, then the stochastic game is completely mixed if and only if the matrix games restricted to states are all completely mixed. Secondly, we identify certain classes of undiscounted zero-sum stochastic games that have stationary optima under specific conditions for individual payoff matrices and transition probabilities. Thirdly, we provide sufficient conditions for discounted as well as certain classes of undiscounted stochastic games to have symmetric optimal/equilibrium strategies—namely, transitions are symmetric and the payoff matrices of one player are the transpose of those of the other. We also provide a sufficient condition for the stochastic game to have a symmetric pure strategy equilibrium. We also provide examples to show the sharpness of our results.