Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder

Models with correlated disorders are rather common in physics. In some of them, like the Aubry-Andr\'e (AA) model, the localization phase diagram can be found from the (self)duality with respect to the Fourier transform. In the others, like the all-to-all translation-invariant Rosenzweig-Porter (TI RP) ensemble or the Hilbert-space structure of the many-body localization, one needs to develop more sophisticated and usually phenomenological methods to find the localization transition. In addition, such models contain not only localization but also the ergodicity-breaking transition, giving way to the non-ergodic extended phase of states with non-trivial fractal dimensions $D_q$. In this work, we suggest a method to calculate both the above transitions and a lower bound to the fractal dimensions $D_2$ and $D_\infty$, relevant for physical observables. In order to verify this method, we apply it to the class of long-range (self-)dual models, interpolating between AA and TI RP ones via both power-law dependences of on-site disorder correlations and hopping terms, and, thus, being out of the validity range of the previously developed methods. We show that the interplay of the correlated disorder and the power-law decaying hopping terms leads to the emergence of the two types of fractal phases in an entire range of parameters, even without having any quasiperiodicity of the AA potential. The analytical results of the above method are in full agreement with the extensive numerical calculations

Utilization of wetland ecosystem through fish-crop diversification for enhanced productivity and economic stability for fish-farm community of Indian sub-continent

This paper deals with a number of case studies that were undertaken during the last 8- 10 years in utilizing divergent æTalÆ wetland ecosystems (deep, semi-deep, temporary in a range of agro-ecological zones like NAZ, OAZ and Coastal Zone of the region) for the development of integrated management programmes using a range of approaches. These included (i) system approach (excavation & renovation, methodological approach), (ii) management (fish-crop management, inter & post-harvest care & processing, marketing), (iii) integrated natural resource management utilizing organic as well inorganic sources, and (iv) low-cost fish-feeds, based on fish-crop diversification. This paper also deals with some endangered indigenous fish species. The unique approach of watershed plans (bherri system), which were formulated for upright production systems, was economically successful. Economic indicators reveal there were comparative advantages of mixed farming systems compared to monoculture, exhibiting less than 2.5 fold gains even for resource poor fish farming families.Fishery management, Resource management

Droplet impact on immiscible liquid pool: Multi-scale dynamics of entrapped air cushion at short timescales

We have detected unique hydrodynamic topology in thin air film surrounding the central air dimple formed during drop impact on an immiscible liquid pool. The pattern resembles spinodal and finger-like structures typically found in various thin condensed matter systems. However, similar structures in thin entrapped gas films during drop impacts on solids or liquids have not been reported to date. The thickness profile and the associated dewetting dynamics in the entrapped air layer are investigated experimentally and theoretically using high-speed reflection interferometric imaging and linear stability analysis. We attribute the formation of multiscale thickness perturbations, associated ruptures, and finger-like protrusions in the draining air film as a combined artifact of thin-film and Saffman-Taylor instabilities. The characteristic length scales depend on the impact Weber number, the ratio of the liquid pool to droplet viscosity, and the ratio of air-water to air-oil surface tension

Fluid dynamics of droplet generation from corneal tear film during non-contact tonometry in the context of pathogen transmission

Noninvasive ocular diagnostics demonstrate a propensity for droplet generation and present a potential pathway of distribution for pathogens such as the severe acute respiratory syndrome coronavirus 2. High-speed images of the eye subjected to air puff tonometry (glaucoma detection) reveal three-dimensional, spatiotemporal interaction between the puff and tear film. The interaction finally leads to the rupture and breakup of the tear film culminating into sub-millimeter sized droplet projectiles traveling at speeds of 0.2 m/s. The calculated droplet spread radius ( ∼ 0.5 m) confirms the likelihood of the procedure to generate droplets that may disperse in air as well as splash on instruments, raising the potential of infection. We provide a detailed physical exposition of the entire procedure using high fidelity experiments and theoretical modeling. We conclude that air puff induced corneal deformation and subsequent capillary waves lead to flow instabilities (Rayleigh-Taylor, Rayleigh-Plateau) that lead to tear film ejection, expansion, stretching, and subsequent droplet formation

Fusion of 6^{6}Li with 159^{159}Tb} at near barrier energies

Complete and incomplete fusion cross sections for $^{6}$Li+$^{159}$Tb have been measured at energies around the Coulomb barrier by the $\gamma$-ray method. The measurements show that the complete fusion cross sections at above-barrier energies are suppressed by $\sim$34% compared to the coupled channels calculations. A comparison of the complete fusion cross sections at above-barrier energies with the existing data of $^{11,10}$B+$^{159}$Tb and $^{7}$Li+$^{159}$Tb shows that the extent of suppression is correlated with the $\alpha$-separation energies of the projectiles. It has been argued that the Dy isotopes produced in the reaction $^{6}$Li+$^{159}$Tb, at below-barrier energies are primarily due to the $d$-transfer to unbound states of $^{159}$Tb, while both transfer and incomplete fusion processes contribute at above-barrier energies.Comment: Phys. Rev. C (accepted