Short-Term Variability of Atmospheric Tides in Earth’s Mesosphere and Lower Thermosphere Region

In the early 2000’s, advances in satellite observations and the development of whole atmosphere models led to a paradigm shift in our understanding of what drives space climate/weather in near-Earth space. In addition to solar and magnetospheric driving influences from above, it was realized that meteorological events (such as changes in convection, tropical cyclones, sudden stratospheric warmings, El Niño, to name just a few) are important drivers of space climate/weather due to the generation and upward propagation of atmospheric waves (tides, planetary waves (PW), and gravity waves (GW)) from lower atmospheric sources. Atmospheric tides are key to understanding the global-scale connection between tropospheric/stratospheric weather/climate and space weather/climate in the mesosphere and lower thermosphere (MLT) region and further above in the ionosphere-thermosphere (IT) region, including dynamo processes. Much progress has been made in delineating and understanding the “tidal climate” of the MLT region, i.e., tidal variability on seasonal or longer timescales. Tidal variability on shorter timescales, however, is much less understood, mainly due to the observational constraints imposed by satellite local solar time sampling.This thesis presents a study of the causes of the “tidal weather” or short-term (day-to-day to intraseasonal, i.e., \u3c90-day) tidal variability from satellite observations in the MLT region in connection to lower atmospheric driving. The tidal baseline data used is based on the “tidal deconvolution” approach performed on 18 years of daily tidal temperature tides observed by the SABER instrument onboard the TIMED satellite. In addition, SD-WACCMX tidal simulations are used to get further insights into the results obtained from the SABER observations. This allows one to resolve non-linear tidal-PW interactions that cause tidal variability on a \u3c30-day timescale, and variability on a 30-90-day timescale that occurs as a response to the recurring Madden-Julian Oscillation (MJO) in tropical convection. This research mainly focuses on two prominent diurnal (D, ~24 hours period) tides which are the westward-propagating (W) zonal wave number 1 (DW1) and the eastward-propagating (E) nonmigrating diurnal tide zonal wave number 3 (DE3) tides, originating from tropospheric radiative and latent heating distributions. The results in this thesis contribute toward a better understanding of the physical causes of day-to-day to intraseasonal (\u3c90-day) variability in the DW1 and DE3 tides and shed new light on how various propagation and forcing conditions– such as the stratospheric Quasi-Biennial Oscillation (QBO), El Niño and La Niña, MJO and the solar cycle – impact short-term tidal variability. The thesis first discusses the use of an information-theoretic approach from climate science for the statistical characterization of the \u3c30-day short-term tidal variability and proceeds to the regression analysis of multi-year variations in the Sun-Earth system to delineate causes of such characteristics. A key result is that the teleconnection effects due to the QBO in the tropical stratosphere coupled with the solar cycle through the polar vortex disturbances change the \u3c30-day short-term tidal variability. This was not previously known. In the second segment of the thesis, the analysis focuses on the intraseasonal timescale of the tidal variability, where a statistical analysis of SABER observations and SD-WACCMX simulations reveals how the MLT tides respond to the various locations of active-MJO events over the Indian and Pacific Oceans. This confirmed previously unverified model predictions of a 10-25% tidal modulation by the MJO as a function of MJO-locations up to the MLT region. The tides largely respond to the MJO in the tropospheric tidal forcing, and the tidal advection and GW drag forcing in the MLT region. Filtering by tropospheric/stratospheric background winds is comparatively less important. These findings have broader implications as tides can also couple variability on PW and MJO timescales from the MLT region to the IT through dynamo processes, which is important for a better understanding and prediction of space weather

Universal adjacency spectrum of (proper) power graphs and their complements on some groups

The power graph $\mathscr{P}(G)$ of a group $G$ is an undirected graph with all the elements of $G$ as vertices and where any two vertices $u$ and $v$ are adjacent if and only if $u=v^m$ or $v=u^m$, $m \in$ $\mathbb{Z}$. For a simple graph $H$ with adjacency matrix $A(H)$ and degree diagonal matrix $D(H)$, the universal adjacency matrix is $U(H)= \alpha A(H)+\beta D(H)+ \gamma I +\eta J$, where $\alpha (\neq 0), \beta, \gamma, \eta \in \mathbb{R}$, $I$ is the identity matrix and $J$ is the all-ones matrix of suitable order. One can study many graph-associated matrices, such as adjacency, Laplacian, signless Laplacian, Seidel etc. in a unified manner through the universal adjacency matrix of a graph. Here we study universal adjacency eigenvalues and eigenvectors of power graphs, proper power graphs and their complements on the group $\mathbb{Z}_n$, dihedral group ${D}_n$, and the generalized quaternion group ${Q}_n$. Spectral results of no kind for the complement of power graph on any group were obtained before. We determine the full spectrum in some particular cases. Moreover, several existing results can be obtained as very specific cases of some results of the paper

Towards Asynchronous Simulations of Turbulent Flows: Accuracy, Performance, and Optimization

Our understanding of turbulence has heavily relied on high-fidelity Direct Numerical Simulations (DNS) that resolve all dynamically relevant scales. But because of the inherent complexities of turbulent flows, these simulations are computationally very expensive and practically impossible at realistic conditions. Advancements in high performance computing provided much needed boost to the computational resources through increasing levels of parallelism and made DNS realizable, even though only in a limited parameter range. As the number of processing elements (PEs) in parallel machines increases, the penalties incurred in current algorithms due to necessary communications and synchronizations between PEs to update data become significant. These overheads are expected to pose a serious challenge to scalability on the next-generation exascale machines. An effective way to mitigate this bottleneck is through relaxation of strict communication and synchronization constraints and proceed with computations asynchronously i.e. without waiting for updated information from the other PEs. In this work, we investigate the viability of such asynchronous computing using high-order Asynchrony-Tolerant (AT) schemes for accurate and scalable simulations of reacting and non-reacting turbulence at extreme scales. For this, we first assess the important numerical properties of AT schemes, including conservation, stability, and spectral accuracy. Through rigorous mathematical analysis, we expose the breakdown of the standard von Neumann analysis for stability of multi-level schemes, even for widely used synchronous schemes. We overcome these limitations through what we call the generalized von Neumann analysis that is then used to assess stability of the AT schemes. Following which, we propose and implement two computational algorithms to introduce asynchrony in a three-dimensional compressible flow solver. We use these to perform first of a kind asynchronous simulation of compressible turbulence and analyze the effect of asynchrony on important physical characteristics of turbulence. Specifically we show that both large-scale and scale-scale features including highly intermittent instantaneous events, are accurately resolved by these algorithms. We also show excellent strong and weak scaling of asynchronous algorithms up to a processor count of P = 262144 because of significant reduction in communication overheads. As a precursor to the development of asynchronous combustion codes for simulations of more challenging problems with additional physical and numerical complexities, we investigate the effect of asynchrony on several canonical reacting flows. Furthermore, for problems with shocks and discontinuities, such as detonations, we derive and verify AT-WENO (weighted essentially non-oscillatory) schemes. With the ultimate goal to derive new optimal AT schemes we also develop a unified framework for the derivation of finite difference schemes. We show explicit trade-offs between order of accuracy, spectral accuracy and stability under this unifying framework, which can be exploited to devise very accurate numerical schemes for asynchronous computations on extreme scales with minimal overheads

Comparative study of the effectiveness of two different dosage of sublingual misoprostal for cervical ripening before hysteroscopy

Background: Hysteroscopy a minimally invasive approach for evaluating uterine cavity, and has become an indispensable diagnostic and therapeutic procedure. The main limiting factor while performing office hysteroscopy is the level of pain or discomfort encountered during the procedure. The pain is attributed mainly to the difficulty in entering the internal cervical os with the hysteroscope and while distending uterine cavity. It could be reduced if cervix is ripened before the procedure. The purpose of this prospective observational study was to compare the effectiveness, adverse effects and surgery-related complications associated with two different doses of sublingual Misoprostol (100 and 200 µg) given 2-4 hours before hysteroscopy.Methods: A randomised comparative study was conducted in the department of Obstetrics and Gynaecology of ABVIMS and Dr. RML hospital New Delhi, from 1st November, 2018 to 31st March, 2020. One hundred and twenty women, fulfilling inclusion criteria were subjected to hysteroscopy. Women received either 100 µg (Group I) or 200 µg (Group II) of sublingual Misoprostol 2-4 hours prior to hysteroscopy. The primary outcome of the study was cervical dilatation as measured by the largest number of Hegar dilator that could be inserted without resistance at the beginning of procedure. The largest dilator that negotiated cervical canal without resistance at the beginning of procedure was recorded as the baseline cervical width. The secondary outcomes were subjective assessment of the surgeon of the ease of dilatation of cervix and adverse effects of drug (i.e. vaginal bleeding, shivering, fever and pain as measured on visual analog scale).Results: The mean baseline cervical width as measured by first Hegar dilator that could be passed through the cervical canal without resistance was 6.6±0.62 mm in group I and 6.94±1.21 mm in group II respectively                    (p value=0.016). Adverse effects like vaginal bleeding, shivering was more in group II compared to group I. No statistically significant difference was found between group I and II with regards to visual analog scale.Conclusions: 100 µg Misoprostol can be used for cervical ripening prior to hysteroscopy with minimal adverse effects

Quantum Zeno effect: a qutrit controlled by a qubit

For a three-level system monitored by an ancilla, we show that quantum Zeno effect can be employed to control quantum jump for error correction. Further, we show that we can realize cNOT gate, and effect dense coding and teleportation. We believe that this work paves the way to generalize the control of a qudit

Double-toric code

We construct a double-toric surface code by exploiting the planar tessellation using a rhombus-shaped tile. With n data qubits, we are able to encode at least n/3 logical qubits or quantum memories. By a suitable arrangement of the tiles, the code achieves larger distances, leading to significant error-correcting capability. We demonstrate the robustness of the logical qubits thus obtained in the presence of external noise. We believe that the optimality of the code presented here will pave the way for design of efficient scalable architectures