Interval type-2 fuzzy automata and Interval type-2 fuzzy grammar

The purpose of the present work is to introduce and study the concept of interval type-2 (IT2) fuzzy grammar which recognizes the given IT2 fuzzy languages. The relationship between IT2 fuzzy automata and IT2 fuzzy (weak) regular grammars is discussed. Specifically, the results we obtained here are (i ) IT2 fuzzy weak regular grammar and IT2 fuzzy regular grammar generate the same classes of IT2 fuzzy languages (ii ) for a given IT2 fuzzy regular grammars, there exists an IT2 fuzzy automata such that they accept the same IT2 fuzzy languages, and vice versa. In addition, we define some operations on IT2 fuzzy languages and it is shown that IT2 fuzzy languages recognized by IT2 fuzzy automata are closed under the operations of union, intersection, concatenation and Kleene closure, but are not closed under complement

A critical layer model for turbulent pipe flow

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating modes, permitting comparison of our results to experimental data, and identify the steady component of the velocity field that varies only in the wall-normal direction as the turbulent mean profile. The "optimal" forcing shape, that gives the largest velocity response, is assumed to lead to modes that will be dominant and hence observed in turbulent pipe flow. An investigation of the most amplified velocity response at a given wavenumber-frequency combination reveals critical layer-like behaviour reminiscent of the neutrally stable solutions of the Orr-Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely a wall layer that scales with $R^{+1/2}$ and a critical layer, where the propagation velocity is equal to the local mean velocity, that scales with $R^{+2/3}$ in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall.Comment: Submitted to the Journal of Fluid Mechanics and currently under revie

On the design of optimal compliant walls for turbulence control

This paper employs the theoretical framework developed by Luhar et al. (J. Fluid Mech., 768, 415-441) to consider the design of compliant walls for turbulent skin friction reduction. Specifically, the effects of simple spring-damper walls are contrasted with the effects of more complex walls incorporating tension, stiffness and anisotropy. In addition, varying mass ratios are tested to provide insight into differences between aerodynamic and hydrodynamic applications. Despite the differing physical responses, all the walls tested exhibit some important common features. First, the effect of the walls (positive or negative) is greatest at conditions close to resonance, with sharp transitions in performance across the resonant frequency or phase speed. Second, compliant walls are predicted to have a more pronounced effect on slower-moving structures because such structures generally have larger wall-pressure signatures. Third, two-dimensional (spanwise constant) structures are particularly susceptible to further amplification. These features are consistent with many previous experiments and simulations, suggesting that mitigating the rise of such two-dimensional structures is essential to designing performance-improving walls. For instance, it is shown that further amplification of such large-scale two-dimensional structures explains why the optimal anisotropic walls identified by Fukagata et al. via DNS (J. Turb., 9, 1-17) only led to drag reduction in very small domains. The above observations are used to develop design and methodology guidelines for future research on compliant walls

The diversity of Indian Brachionidae (Rotifera: Eurotatoria: Monogononta) and their distribution

We evaluate diversity status of the Brachionidae of India and present an annotated checklist of 46 species excluding dubious and unconfirmed reports. These merit biodiversity value as ~27% of the global diversity of the taxon and ~81% of its Oriental species. We observed two Australasian elements, two Oriental endemics, one Indian endemic, one paleotropical and one cosmo (sub) tropical species. The cold-water Keratella serrulata and Notholca squamula are new records from eastern Himalayas. Maximum brachionid diversity (32 species) from Assam state of northeast India (NEI) is followed by the reports of 27 and 26 species from Tamil Nadu and West Bengal, respectively; 25 species each from Tripura and Maharashtra; and 24 species from Jammu & Kashmir. Brachionus, the most diverse brachionid genus, is widely distributed in India with low richness in hill states of NEI and coastal waters in particular. The Indian brachionid taxonomy is confounded with unconfirmed reports, misidentifications, invalid taxa, and inconsistent treatment of morphological variants, while analysis of cryptic diversity in Brachionus calyciflorus, B. caudatus, B. forficula, B. plicatilis, B. quadridentatus, B. urceolaris, Keratella cochlearis and K. quadrata species-groups awaits attention