Department of Computer Science and Engineering

National Capital Region (NCR, Delhi) in India is one of the fastest-growing metropolitan cities which is facing a severe water crisis due to increasing water demand. The over-extraction of groundwater, particularly from its unconsolidated alluvial deposits makes the region prone to subsidence. In this study, we investigated the effects of plummeting groundwater levels on land surface elevations in Delhi NCR using Sentinel-1 datasets acquired during the years 2014–2020. Our analysis reveals two distinct subsidence features in the study area with rates exceeding 11 cm/year in Kapashera—an urban village near IGI airport Delhi, and 3 cm/year in Faridabad throughout the study period. The subsidence in these two areas are accelerating and follows the depleting groundwater trend. The third region, Dwarka shows a shift from subsidence to uplift during the years which can be attributed to the strict government policies to regulate groundwater use and incentivizing rainwater harvesting. Further analysis using a classified risk map based on hazard risk and vulnerability approach highlights an approximate area of 100 square kilometers to be subjected to the highest risk level of ground movement, demanding urgent attention. The findings of this study are highly relevant for government agencies to formulate new policies against the over-exploitation of groundwater and to facilitate a sustainable and resilient groundwater management system in Delhi NCR.

We investigate the flow within a liquid-metal battery induced by an externally imposed magnetic field, B0. An analytical model for laminar flow is proposed and this is found to be in excellent agreement with numerical simulations, not only for weakly forced steady flow, but also for the time-averaged velocity in more strongly forced flows where the motion is either unsteady (but laminar) or else weakly turbulent. Our primary conclusion is that surprisingly weak magnetic fields are capable of destabilizing the flow and inducing turbulence, with turbulence first appearing at B0≈1.0G. By comparison, the earth's magnetic field is ∼0.5 G. This extreme sensitivity of liquid-metal pools carrying current to an external magnetic field has long been known in the context of other industrial processes.

This study evaluates the impact of land surface models (LSMs) and urban heterogeneity [using local climate zones (LCZs)] on air temperature simulated by the Weather Research and Forecasting model (WRF) during a regional extreme event. We simulated the 2017 heatwave over Europe considering four scenarios, using WRF coupled with two LSMs (i.e., Noah and Noah-MP) with default land use/land cover (LULC) and with LCZs from the World Urban Database and Access Portal Tools (WUDAPT). The results showed that implementing the LCZs significantly improves the WRF simulations of the daily temperature regardless of the LSMs. Implementing the LCZs altered the surface energy balance partitioning in the simulations (i.e., the sensible heat flux was reduced and latent heat flux was increased) primarily due to a higher vegetation feedback in the LCZs. The changes in the surface flux translated into an increase in the simulated 2-m relative humidity and 10-m wind speed as well as changed air temperature within cities section and generated a temperature gradient that affected the temperatures beyond the urban regions. Despite these changes, the factor separation analysis indicated that the impact of LSM selection was more significant than the inclusion of LCZs. Interestingly, the lowest bias in temperature simulations was achieved when WRF was coupled with the Noah as the LSM and used WUDAPT as the LULC/urban representation.

Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. Besides being a natural and fundamental question in computer algebra on its own, fast algorithms for this problem are also closely related to fast algorithms for other natural algebraic questions like polynomial factorization and modular composition. And while nearly linear time algorithms have been known for the univariate instance of multipoint evaluation for close to five decades due to a work of Borodin and Moenck, fast algorithms for the multivariate version have been much harder to come by. In a significant improvement to the state of art for this problem, Umans and Kedlaya & Umans gave nearly linear time algorithms for this problem over field of small characteristic and over all finite fields respectively, provided that the number of variables n is at most do(1) where the degree of the input polynomial in every variable is less than d. They also stated the question of designing fast algorithms for the large variable case (i.e. n ‰ do(1)) as an open problem. In this work, we show that there is a deterministic algorithm for multivariate multipoint evaluation over a field Fq of characteristic p which evaluates an n-variate polynomial of degree less than d in each variable on N inputs in time (N + dn)1 + o(1)(logq, d, n, p)provided that p is at most do(1), and q is at most (exp(g (exp(d)))), where the height of this tower of exponentials is fixed. When the number of variables is large (e.g. n ‰ do(1)), this is the first nearly linear time algorithm for this problem over any (large enough) field. Our algorithm is based on elementary algebraic ideas and this algebraic structure naturally leads to the following two independently interesting applications. We show that there is an algebraic data structure for univariate polynomial evaluation with nearly linear space complexity and sublinear time complexity over finite fields of small characteristic and quasipolynomially bounded size. This provides a counterexample to a conjecture of Milterson who conjectured that over small finite fields, any algebraic data structure for polynomial evaluation using polynomial space must have linear query complexity. We also show that over finite fields of small characteristic and quasipolynomially bounded size, Vandermonde matrices are not rigid enough to yield size-depth tradeoffs for linear circuits via the current quantitative bounds in Valiant's program. More precisely, for every fixed prime p, we show that for every constant "> 0, and large enough n, the rank of any n × n Vandermonde matrix V over the field pa can be reduced to (n/exp(ω((")logn))) by changing at most n(") entries in every row of V, provided a ≤ (logn). Prior to this work, similar upper bounds on rigidity were known only for special Vandermonde matrices. For instance, the Discrete Fourier Transform matrices and Vandermonde matrices with generators in a geometric progression.