Activity induced phase separation and the emergence of liquid crystal phases in chiral and achiral systems, and development of an efficient method to compute the entropy of various liquid crystal phases

The phase behaviour of shape-anisotropic particles is an emerging field of research that gives rise to various liquid crystal phases. In this thesis, we explore various equilibrium and non-equilibrium properties of shape-anisotropic particles by modelling them as soft repulsive spherocylinders (SRSs) and soft helical rods. In the first part, we introduce the two-temperature model to study the phase behaviour of scalar active SRS and soft helical rods. Most realisations of activity are vectorial in nature due to the force of self-propulsion. Recent studies have shown that many physical and biological processes, like phase separation in colloidal systems, chromatin organisation in the nucleus, are operated by the unequal sharing of energy by the constituents of the system. Such systems are classified as scalar active systems. In the simplest case, these systems can be modelled by connecting half the particles with a thermostat of higher temperature (labelled ‘hot’/‘active’) while maintaining temperature of the rest constant (labelled ‘cold’/‘passive’) at a lower value. The relative temperature difference between the two constituents of the system is a measure of activity. This model is known as two-temperature model that has been found to capture many essential properties of scalar activity. Starting from a homogeneous isotropic phase at a definite temperature, we show that this model leads to phase separation into hot and cold regions and induces liquid-crystal ordering of the cold particles while hot particles remain in the isotropic phase. In particular, we find that activity drives the cold particles through a phase transition to a more ordered state and the hot particles to a state of less order compared to the initial equilibrium state. Hence, the phase boundary of the isotropic-nematic transition shifts towards lower densities for cold particles and higher densities for the hot particles with respect to its equilibrium location. Remarkably, we find liquid crystalline phases for the aspect ratios [length(L)/diameter(D)] as low as L/D = 2, 3 which do not satisfy the minimum shape-anisotropy criteria that Onsager’s theory demands in equilibrium. Similar model we have employed in a system of soft helical particles of various intrinsic chiralities and found different liquid crystal ordering in these cases as well. The following nonequilibrium features emerge from our study: an enhancement of the temperature of half of the particles gives rise to LC ordering in the remaining half of the particles at any density. The hot and cold domains should not be viewed as bulk equilibrium phases with non-equilibrium behaviour only at the interfaces. By calculating the stress anisotropy and heat current, we find that the non-equilibrium behaviour is not restricted to the hot-cold interfaces but pervades the system as a whole, driving various ordering transitions in the cold zone. Thus, our study unravels various aspects of non-equilibrium scalar active rods in the framework of the two-temperature model. In the second part, we discuss the Two-phase thermodynamic (2PT) model for computing entropy, free energy, and other thermodynamic properties of various liquid crystal phases in equilibrium. In the 2PT method, the density of state (DoS) of the LC phases is decomposed into vibrational (solid) and diffusive (gas) components. The thermodynamic quantities are then calculated using harmonic oscillator approximations for the solid component, hard sphere approximations for the gas component, and the rigid rotor approximation for the rotational mode. In the 2PT method, the entropy of a definite state point is calculated from a single MD trajectory, which makes it advantageous for systems for which the analytical form of the equation of state is unknown (such as SRS). Our method can be used to calculate entropy and other thermodynamic quantities of different liquid crystal phases formed by the SRS system.Inspire fellowshi

Wetting and Frictional Properties of Hexagonal Boron Nitride with Atomic-Scale Defects and Roughness

Two-dimensional (2D) materials such as graphene, hexagonal boron nitride (hBN), and molybdenum disulfide (MoS2) have become materials of choice for applications spanning optoelectronics, atomically thin coatings, and high-throughput and high-selectivity membranes. In such applications, the exposure of 2D materials (e.g., hBN) to liquids underscores the importance of understanding 2D material-liquid interactions. Wettability is one of the important interfacial properties of 2D materials such as hBN, and understanding it is vital for designing devices for seawater desalination and osmotic power harvesting. The contact angle of water is the fundamental property measured in experimental investigations on wettability; so far, however, studies have not considered the effect of defects on the water contact angle on hBN surfaces. In this thesis, we simulated the wetting behaviour of water on monolayer and bulk hBN, in their pristine and defective forms, using classical molecular dynamics simulations supported by quantum-mechanical density functional theory calculations. We considered five defect topologies – the B, N, BN, B2N, and B3N vacancy defects – and also studied the effect of the defect concentration on the water contact angle to investigate more realistically the interfacial properties of defective hBN. We found that defects at a concentration of 0.082 nm-2 no longer affect the wetting properties of hBN surfaces. While bulk hBN, modeled as a stack of four monolayers, showed hydrophilic behavior, monolayer hBN exhibited hydrophobic behaviour. Additionally, hBN surfaces containing B and B2N vacancies exhibited increased hBN-water electrostatic interactions, especially at a higher vacancy concentration of 0.328 nm-2. We found that the presence of surface roughness, but not that of vacancy defects, leads to remarkable agreement with the experimentally observed water contact angle of 66° on freshly synthesized, uncontaminated hBN. Additionally, the inclusion of surface roughness accurately predicts the experimental water slip length of ~1 nm on hBN. Our results underscore the importance of considering realistic 2D materials with surface roughness models while modeling nanomaterial-water interfaces in molecular simulations

Interaction of distinguished varieties and the Nevanlinna-Pick interpolation problem in some domains

This thesis explores the interplay between complex geometry and operator theory, focusing on characterizing certain objects from algebraic geometry. Two concepts that have been of prime importance in recent times in the analysis of Hilbert space operators are distinguished varieties, which are a priori geometric in nature, and joint spectra, which are a priori algebraic in nature. This thesis brings them together to characterize all distinguished varieties with respect to the bidisc, more generally the polydisc and the symmetrized bidisc in terms of the joint spectrum of certain linear pencils. Some of the results are shown to refine earlier work in these directions. The binding force is provided by an operator-theoretic result, the Berger-Coburn-Lebow characterization of a tuple of commuting isometries. The thesis then turns to studying the uniqueness of solutions of the solvable NevanlinnaPick interpolation problems on the symmetrized bidisc and its connection with distinguished varieties. Several sucient conditions have been identified for a given data to have a unique solution. Moreover, for a class of solvable data on the symmetrized bidisc, there exists a distinguished variety where all solutions agree. Additionally, the thesis explores the more general concept of the determining sets

Towards Robustness of Neural Legal Judgement System

Legal Judgment Prediction (LJP) implements Natural Language Processing (NLP) techniques to predict judgment results based on fact description. It can play a vital role as a legal assistant and benefit legal practitioners and regular citizens. Recently, the rapid advances in transformer- based pre-trained language models led to considerable improvement in this area. However, empirical results show that existing LJP systems are not robust to adversaries and noise. Also, they cannot handle large-length legal documents. In this work, we explore the robustness and efficiency of LJP systems even in a low data regime. In the first part, we empirically verify that existing state-of-the-art LJP systems are not robust. We further provide our novel architecture for LJP tasks which can handle extensive text lengths and adversarial examples. Our model performs better than state-of-the-art models, even in the presence of adversarial examples of the legal domain. In the second part, we investigate the approach for the LJP system in a low data regime. We further divide our second work into two scenarios depending on the number of unseen classes in the dataset which is being used for the LJP system. In the first scenario, we propose a few-shot approach with only two labels for the Judgement prediction task. In the second scenario, we propose an approach where we have an excessive number of labels for judgment prediction. For both approaches, we provide novel architectures using few-shot learning that are also robust to adversaries. We conducted extensive experiments on American, European, and Indian legal datasets in the few-shot scenario. Though trained using the few-shot approach, our models perform comparably to state-of-the-art models that are trained using large datasets in the legal domain

Raman Spectroscopy Instrumentation and Its Application in Deep Tissue Imaging

Raman spectroscopy is based on inelastic scattering, which gives molecular information. Due to its weak nature, for a long-time Raman spectroscopy was limited to only study of molecular interactions, but with the advancement in technology such as highly compact and stable lasers, high quantum efficiency and low noise detectors and so on, Raman spectroscopy today finds itself in wide applications ranging from study on biological cells to space applications. In the first work we aim to develop a 3D Raman imaging system that can give both chemical and morphological information of the concealed object using Universal Multiple Angle Raman spectroscopy (UMARS). Spatial offset Raman spectroscopy (SORS) is a widely used Raman technique and they can obtain Raman signals upto depth of 5 cm. Using UMARS technique we were able to demonstrate that we could obtain Raman signals of deeply buried objects (>5 cm). In the second work, we developed a 3D Raman Monte Carlo model for the UMARS experiments. The model was developed to simulate light propagation inside a chicken tissue with an ellipsoid object containing different chemicals embedded inside it. The 2D Raman intensity map obtained in this simulation was compared to the 2D Raman intensity map obtained by experiments and they were found to be in agreement. In the third work, we developed a low cost (< 4lakhs INR), portable (30×30cm), high throughput (f/3) and minimum optical aberration Raman spectrometer. In the fourth work, we developed a novel spectrometer design. Unlike current diffraction grating based spectrometer, this novel spectrometer utilizes multi diffraction orders. This design can be operated in an optical addition mode, where the different orders (+1 and -1) of the diffraction grating are focused onto the same detector plane such that the same wavelengths of both the order are optically combined to yield better signal to noise ratio. In another mode, this spectrometer records different wavelength range of the diffracted orders onto the detector, thus obtaining a long range spectrum without the need for a complex mechanism for rotating the grating. In the fifth and final work, we developed a low cost charge coupled devices (CCD) data acquisition module for spectroscopy applications. Here a CCD data acquisition system was developed based on field programmable arrays (FPGA)

Neuronal complex bursts and network information transfer in the hippocampus are robust to biophysical heterogeneities

Biological entities must adopt mechanisms to override the impact of external perturbations to achieve stability and robustness. A crucial feature of biological systems is that they exhibit several forms of heterogeneities spanning all scales of functional analysis. A central question on biological robustness is therefore its relationship to heterogeneities, specifically addressing details pertaining to whether biological heterogeneities promote or impede robustness. In this thesis, we chose the mammalian CA3 sub-region of the hippocampus to be the system of interest towards understanding the impact of the biophysical heterogeneities on the functional robustness across the cellular and network scales. Heterogeneities at the cellular scale are associated with the intrinsic properties of the CA3 pyramidal neurons as well as with synaptic inputs. The overall goal here was to assess the robust emergence of neuronal intrinsic properties (input resistance, back-propagating action potential amplitude, bursting and spiking profiles) along with complex spike bursting (CSB) in the CA3 pyramidal neurons with respect to heterogeneities in their parametric and measurement spaces. We generated a heterogeneous population of 12,000 random morphologically and biophysically realistic CA3 pyramidal neurons spanning a broad spectrum of parameters. We found two functional sub-classes of intrinsic bursting and regular spiking neurons, with significant differences in the expression profiles of N-type calcium and calcium-activated potassium (SK) channels. By triggering CSBs in all valid models using a variety of protocols, we observed substantial heterogeneities in the CSB propensities across models and protocols. Employing the virtual knockout approach for 7 different ion channels and N-methyl-D-aspartate receptors individually, we noted that synergistic interactions between several intrinsic and synaptic components regulated the robust emergence of CSB in these neurons. Together, we demonstrate the expression of ion-channel degeneracy in the robust emergence of physiological properties of CA3 pyramidal neurons including CSB, despite pronounced heterogeneities in their intrinsic and synaptic components. Heterogeneities at the network scale are associated with intrinsic and synaptic components, with synaptic heterogeneities spanning local connections as well as afferent inputs from other brain regions. In this part of the thesis, we assessed the impact of neural-circuit heterogeneities, balance between excitatory and inhibitory synaptic strengths, and trial-to-trial variability on the spatial tuning profiles and spatial information transfer in the CA3 recurrent network. We employed homogeneous and heterogenous networks and stimulated them with spatially modulated inputs and employed the stimulus-specific information (SSI) metric to quantify the spatial information transfer by the place cells in these networks. We observed notable heterogeneities in spatial information transfer across both homogeneous and heterogeneous networks, with information transfer also dependent on synaptic inhibition strengths and trial-to-trial variabilities. Strikingly, spatial information transfer was robust to relatively higher noise levels in the heterogeneous networks compared to their homogeneous counterparts, thereby highlighting a crucial role for neural heterogeneities in enhancing the robustness of spatial information transfer in a recurrent place-cell network. We also found that a precise balance between recurrent and afferent connectivity was essential to maintain optimal spatial information transfer in neurons of such networks. Our analyses postulate a critical role for intrinsic heterogeneities in enhancing the robustness of spatial information transfer in a recurrent network of spatially tuned neurons. Together, these analyzes point to a beneficial role for neural heterogeneities in the robustness of single-neuron and network physiology in the CA3 sub-region of the hippocampus

Constrained Stochastic Differential Equations on Smooth Manifolds.

Dynamical systems with uncertain fluctuations are usually modelled using Stochastic Differential Equations (SDEs). Due to operation and performance related conditions, these equations may also need to satisfy the constraint equations. Often the constraint equations are ``algebraic". Such constraint equations along with the given SDE form a system of Stochastic Differential-Algebraic Equations (SDAEs). The main objective of this thesis is to consider these equations on smooth manifolds. However, we first consider SDAEs on Euclidean spaces to understand these equations locally. A sufficient condition for the existence and uniqueness of the solution is obtained for SDAEs on Euclidean spaces. We also give necessary condition for the existence of the solution. Based on the necessary condition, there exists a class of SDAEs for which there is no solution. Since all SDAEs are not solvable, we present methods and algorithms to find approximate solution of the given SDAE. In order to extend this work to smooth manifolds, we consider second order stochastic differential geometry to construct Schwartz morphism to represent SDEs with drift that are driven by p-dimensional Wiener process. We show that it is possible to construct such Schwartz morphisms using what we call as \textit{diffusion generators}. We demonstrate that diffusion generator can be constructed using flow of second order differential equations, in particular using regular Lagrangians. The results obtained for SDAEs on Euclidean spaces are extended to SDAEs on smooth manifolds using the framework of diffusion generators. We show that the results obtained for SDAEs on Euclidean spaces translate to the manifold setting with minimal modifications. We have derived Ito-Wentzell's formula on manifolds in the framework of diffusion generators to obtain approximate bounded solution with unit probability. Another type of approximate solution is bounded solution such that the probability of explosion is bounded by $\alpha<1$. We present algorithms to compute approximate solutions of both type. This has been demonstrated with an example of SDAE on a sphere

Low Head Hydraulic Pumping – Design, Simulation, and Field Validation of Ram and Turbine Pump in Indian River Basin

Water energy is essential for economic expansion and human development. Social progress and economic growth depend on meeting water energy needs sustainably. The use of non renewable energy sources for pumping water to high heads from a low head (surface flow or groundwater) has led to a global imbalance, leaving society vulnerable to an uncertain future. The thesis aims to bypass electrical energy for pumping water in a niche region of people near river basins, promoting interdependence and minimizing consumption. Technical engineering solutions applied in this work use the flow from rivers or streams as their primary input energy sources to pump 5 to 10 percent of the water needed for sustenance at higher elevations while returning 90 to 95 percent of the water that is used for pumping back to the stream. This endeavour has the potential to assist around 5% of the world's population who currently live along the river basins. The Taipadar village case study is illustrated, which is situated in the Tiriya river basin of the Chhattisgarh state, Bastar, in central-east India, to demonstrate the implementation of such technical solutions in the real world. The emphasis is given to the effectiveness of converting two hydraulic powers: input river flow and head and output delivered flow and delivery head. Afterward, in this research, the two appropriate engineering solutions of the Taipadar village, namely the Ram pump and Turbine pump, have been examined for their best performance, and monograms have been created to enable technicians and field personnel to develop their customized systems. A detailed comparison of two technologies (i.e., Ram pump and Turbine pump) is made with a discussion of their working principles and the results of tests conducted at a field station in central-east India. The H-Q-D (Head-Discharge-Diameter) chart is also developed to serve as a helpful tool for interpreting the technology concerning boundary circumstances and serves as a roadmap for upcoming innovations in such renewable hydro pumping devices. It is crucial to investigate the technologies' combined or individual overall optimum performance for the system design. To gain insights into the performance of the turbine pump, its blade geometry, represented by the blade thickness to chord length ratio (t/l), is analysed. This study on t/l highlights its effect on the specific speed of the turbine and, therefore, the pumping efficiency. This comprehensive work on t/l is a novel area of investigation that has been previously ignored or overlooked, but its findings have opened up new avenues for optimizing the performance of hydro turbines. The scaling effect of axial flow propellers while maintaining a constant t/l ratio, as well as varying chord lengths and blade numbers, is also addressed. A comprehensive qualitative theory of energy transfer and corresponding loss mechanisms is also provided, along with an analytical method. Moreover, in order to examine the performance of a hydraulic ram, this study analysed the stroke rate of the impulse valve, as well as the valve setting, drive head, and length, using two analytical models. These models (i.e., Tacke and Iversen) have validated the results that show good conformance with matching delivered flow. The analysis of the effect of control variables on input variables demonstrates that the field setup outperformed the lab setup. 4 The thesis, in the end, will provide the fundamentals, design, conceptualization, construction, evaluation, and field validation guidelines for implementing low-head micro hydro pump technologies to deliver water, generate electricity, and, most notably, convince society and policymakers to shift their current reductionist approach. The scaling and design of the turbine pump, pump selection, and flow output estimation with a technical-economic feasibility study procedure are also discussed

Constraining the Lithium Seawater Mass and Isotope Budget: Diagenetic Processes Through Marine Pore Waters

Silicate weathering consumes CO2 and controls cation fluxes to the ocean, thus playing a critical role in modulating long-term seawater chemistry and climate. There are very few markers of seawater chemistry whose value has changed over time as a function of the uplift – weathering – subduction cycle. Lithium, being one such proxy has been extensively utilized as a geochemical tracer whose long-term evolution in seawater is a function of Urey’s tectonic cycle. Marine pore-waters are an excellent archive to study the sedimentary processes affecting seawater chemistry. Thus, marine pore water Li concentration and isotopes are utilized in elucidating numerous under-constrained diagenetic processes such as marine clay formation, clay transformation, carbonate diagenesis, subduction of slab, and clay dewatering. To constrain the above processes through Li isotopes, we have developed a method for separation of Li from matrix elements using a single-step column chromatography technique and precise measurement of Li isotope ratios using inhouse ICP-QQQ. Some of the features of the developed method are high column recovery 101.0 ± 1.2 % (n = 20), low cumulative Li blank (<0.6 pg) and crustal element blanks (<1.5 ng), high Na tolerance (up to 100:1 of Na:Li), low mass requirement (<0.15 ng per analysis), and a sub-permil precision (±0.6 ‰, 2s). Utilizing the above method, we analysed pore water samples from IODP Leg 339 (Mediterranean outflow) and Leg 379 (Amundsen Sea, Southern Ocean) for Li isotopes to deduce the processes occurring at these sites and its implications on Li seawater budget. At the pore water-sediment interface of continental margins, authigenic alumino-silicate clay (smectite) formation also termed as Reverse Weathering, removes Li from seawater/pore water. The reverse weathering process preferentially uptakes 6Li over 7Li. Thus, pore waters are depleted in Li compared to seawater ([Li]PW δ7LiSW). This process occurs in shallow sediment depths where smectite is the dominant clay and illitization is not commenced. However, most pore water profiles exhibit higher Li concentrations and lighter isotopic compositions indicating clay transformation process. During clay transformation i.e., smectite to illite transformation, owing at high pressure and temperature (150-200 Celsius) during burial, isotopically light Li is released from the clays. This release of isotopically light Li increases the pore water Li concentration while driving it isotopically light. During sediment subduction, a significant fraction of this clay bound isotopically light Li is released as a part of clay dewatering. This thesis investigates IODP Leg 339 pore water samples with clay dewatering evidence (recorded by δ18O of pore waters) and IODP Leg 379 pore water samples in silica-rich environment with high Li concentration and lighter isotopic composition relative to seawater helps us to constrain Li seawater mass budget further. A preliminary set of equations that govern flux of an element between the marine sediments and seawater following the general diagenetic equation (GDE) is also developed in the present work. These equations incorporate the effects of diffusion, advection and reaction kinetics in the sediments and thus, govern the transfer of Li within the sediment column. Flux calculations for 5 IODP sites and 12 from the literature have been included in the work, and the implications of these flux calculations have been discussed in detail. A thorough development of this model will lead to establishing a mass and isotope budget in seawater which will be applicable across elements and processes. This fundamental study of Li seawater chemistry brings us a step closer in understanding the complex dynamics of ocean systems

Leveraging KG Embeddings for Knowledge Graph Question Answering

Knowledge graphs (KG) are multi-relational graphs consisting of entities as nodes and relations among them as typed edges. The goal of knowledge graph question answering (KGQA) is to answer natural language queries posed over the KG. These could be simple factoid questions such as “What is the currency of USA? ” or it could be a more complex query such as “Who was the president of USA after World War II? ”. Multiple systems have been proposed in the literature to perform KGQA, include question decomposition, semantic parsing and even graph neural network-based methods. In a separate line of research, KG embedding methods (KGEs) have been proposed to embed the entities and relations in the KG in low-dimensional vector space. These methods aim to learn representations that can be then utilized by various scoring functions to predict the plausibility of triples (facts) in the KG. Applications of KG embeddings include link prediction and KG completion. Such KG embedding methods, even though highly relevant, have not been explored for KGQA so far. In this work, we focus on 2 aspects of KGQA: (i) Temporal reasoning, and (ii) KG incompleteness. Here, we leverage recent advances in KG embeddings to improve model reasoning in the temporal domain, as well as use the robustness of embeddings to KG sparsity to improve incomplete KG question answering performance. We do this through the following contributions: Improving Multi-Hop KGQA using KG Embeddings We first tackle a subset of KGQA queries – multi-hop KGQA. We propose EmbedKGQA, a method which uses ComplEx embeddings and scoring function to answer these queries. We find that EmbedKGQA is particularly effective at KGQA over sparse KGs, while it also relaxes the requirement of answer selection from a pre-specified local neighborhood, an undesirable constraint imposed by GNN-based for this task. Experiments show that EmbedKGQA is superior to several GNN-based methods on incomplete KGs across a variety of dataset scales. Question Answering over Temporal Knowledge Graphs We then extend our method to temporal knowledge graphs (TKG), where each edge in the KG is accompanied by a time scope (i.e. start and end times). Here, instead of KGEs, we make use of temporal KGEs (TKGE) to enable the model to make use of these time annotations and perform temporal reasoning. We also propose a new dataset - CronQuestions - which is one of the largest publicly available temporal KGQA dataset with over 400k template-based temporal reasoning questions. Through extensive experiments we show the superiority of our method, CronKGQA, over several language-model baselines on the challenging task of temporal KGQA on CronQuestions. Sequence-to-Sequence Knowledge Graph Completion and Question Answering So far, integrating KGE into the KGQA pipeline had required separate training of the KGE and KGQA modules. In this work, we show that an off-the-shelf encoder-decoder Transformer model can serve as a scalable and versatile KGE model obtaining state-of-the-art results for KG link prediction and incomplete KG question answering. We achieve this by posing KG link prediction as a sequence-to-sequence task and exchange the triple scoring approach taken by prior KGE methods with autoregressive decoding. Such a simple but powerful method reduces the model size up to 98% compared to conventional KGE models while keeping inference time tractable. It also allows us to answer a variety of KGQA queries, not being restricted by query type