Indian Institute of Science Bangalore
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Exploring Soft Matter and Modified-Liquid Electrolytes for Alkali metal (Li, Na) Based Rechargeable Batteries
No full textThe current upsurge in demand for high energy density batteries for applications across industries ranging from small scale portable electronics, electric automobiles to storage grids, has led to research in next generation, beyond lithium -ion batteries. Alkali metals like lithium and sodium, by virtue of their high theoretical capacity (3860 mAhg-1 for Li and 1165 mAhg-1 for Na) and low electrochemical potentials, are most suitable anodes for producing high energy density batteries. The vigorous reactivity, unstable solid-electrolyte interface and dendrite formation are some of the major hurdles towards use of lithium and sodium as anodes in a conventional liquid electrolyte battery. A well designed and optimised electrolyte plays a paramount role towards safe operation of an alkali metal battery. In the present thesis, we have explored few free-standing, mechanically stable plasticised gel polymer electrolytes (GPE) for lithium and sodium metal battery which has been demonstrated to have a good ionic conductivity with very stable interfacial properties and suppressed dendrite growth. A spectroscopic investigation into the ion-conduction mechanism in a concentrated lithium gel polymer electrolyte system has also been described in detail. Along with the stable performance of alkali metal batteries with the designed GPEs, we have also ventured into few high-capacity cathodes like sulphur and oxygen using modified electrolytes
Development of multifunctional polydimethylsiloxane-based polyurethanes as an ‘off-the-shelf’ alloplastic platform for urological reconstruction
No full textOver 400 million patients suffer from urinary bladder-associated physiological disorders
globally, which often necessitate surgical intervention for a reconstructive procedure. The
current gold standard for bladder reconstruction, an autologous graft, is proven not to be an
ideal substitute in clinics. Such unmet clinical needs drive the continuous surge for structural
and functional substitutes of urinary tissues, including ureters, bladder-wall, and urethra.
Against this backdrop, the present dissertation explores a biomaterial-based, functionalised
alloplastic platform for urological reconstruction. This strategy for an alloplastic urinary tissue
encompasses a biostable, 'off-the-shelf' available therapeutic option that simplifies and shortens
surgical treatment. Furthermore, it presents the potential to evade the challenges and
complications of autografts and scaffold-based regenerative techniques.
Considering the prerequisites of a urological alloplast, the combination of
polydimethylsiloxane and thermoplastic polyurethanes (TPU/PDMS) is deemed most
advantageous. The synergistic integration of varying contents of PDMS within the molten TPU
matrix is realised through a processing methodology of dynamic vulcanisation (DV). The
experimental outcomes are evaluated and correlated with different phenomenological models
to understand DV induced strengthening of structure. The theoretical predictions, in
conjunction with material property characterisation, allow a better understanding of the
improved interfacial behaviour and superior performance of the crosslinked polymer system.
The in situ compatibilised blends are further investigated for clinically relevant viscoelastic
properties to sustain high pressure, large distensions, and surgical handling/manipulation.
Moreover, non-exhaustive chemical strategies are harnessed to counter urinary tract infections
through the covalent incorporation of polycationic moieties. The new generation alloplasts,
endowed with contact killing surfaces, are assessed for their efficacy in pathogenically infected
artificial urine. In addition, the adhesion and proliferation of murine fibroblasts on different
polymeric compositions to establish their cytocompatibility.
Building further upon the knowledge of the antibacterial and antifouling activity of
polycationic modifications, layer-by-layer (LbL) assembled multifunctional surface grafting
are conceived to sustain long-term stability in a urinary environment, to suppress encrustation
and biofilm formation. The performance of the single-step and LbL-grafted blends is
benchmarked against the conventional urological alloplasts, using a customised lab-scale
bioreactor set-up. Post-six weeks of incubation in the dynamic assembly simulating ureasepositive microbial infection, the contact-active blends exhibited a remarkable ability to resist
calcium and magnesium encrustation, while retaining adequate grafting integrity. As high as
4-fold log reduction in the planktonic growth of bacterial strains associated with bladder stones
and renal calculi is recorded. In vitro cellular assessment is carried out with human
keratinocytes and human embryonic kidney cells to evaluate the cytocompatibility of the
surface grafted blends against the medical-grade control polymer. Finally, the optimum LbL
grafted formulations are investigated for their performance in a phase-I pre-clinical study
utilising human urine samples collected from 129 patients. The newly developed blends meet
the clinically desirable attributes and present a strong potential as a stable, contact-active, antiencrustation biomaterial platform for urinary implantation.
Summarising, this dissertation contemplates the new-generation, infection and encrustationresistant alloplasts. In pursuit of this vision, multifunctional polymeric biomaterials are
designed to sustain desirable performance in a urinary environment. These next-gen
biomaterials pave the way for an alloplastic platform that can integrate into clinical practice to
improve the quality of modern urological treatment
Design and development of lateral force-controlled tribosystems
No full textIn a tribo-system, the frictional resistance during a sliding process depends on several parameters. These parameters include the interacting materials, their surface topography, contact conditions such as normal load, sliding speed, contact pressure and the nature of lubrication at the interface. In addition, the dynamics of the tribo-system become important as it influences the nature of the asperity interaction at the sliding interface. The dynamics of a tribo-system is governed by the various forces in the system. For a given external loading and surfaces, changing the system's mass, stiffness, and damping changes the inertial, spring and damping forces in the tribo-system. This result in different accelerations and relative sliding velocities at the interface, and the asperities of the two surfaces would interact at different rates. Thus changing the system parameters (mass, stiffness and damping) would result in a different frictional response for given surfaces and external forcing. Therefore, it is important to consider these parameters (mass, stiffness and damping) during the tribometer design stage so that the tribo-system is close to the actual tribo-system to be studied.
Now, based on these three parameters (mass, stiffness and damping) and the surface topography of the interacting surfaces, we propose that a tribo-system can be classified as a Lateral Force Controlled (LFCS) and a Lateral Displacement Controlled System (LDCS). The principle difference between the two types of tribo-systems is the nature of the asperities interaction during the sliding motion. At the asperity level, in LDCS, two surfaces are constrained to move at a certain velocity, forcing the asperities to shear at the specified rate. The resistance to the motion is measured by measuring the frictional force using load cells. Contrary to this, in LFCS, a known tangential force is applied, and the surfaces (bodies) are allowed relative motion under the applied force. Therefore, in LFCS, it is not the velocity but rather the acceleration (rate of change of velocity) which dictates the nature of asperity interaction and the frictional response. In this regard, the surface topography of the two interacting surfaces plays a crucial role in dictating the interaction rate and the frictional response during sliding. If there is a continuous change in the real area of contact during the sliding motion, the interaction of asperities at contact is analogous to intermittent loading. The loading frequency of the asperities depends upon the surface topography and the sliding speed at the interface. If this loading frequency of asperities matches the system's natural frequency, the structure's vibration magnitude increases. These conditions exist at very low sliding velocities, especially during the start and stop of the motion. In lubricated contacts, such conditions exist in the boundary lubrication regime of the Stribeck curve. At such lower speeds, the system is predominantly a force-controlled system instead of a displacement-controlled one. Under these conditions, contact stiffness is critical and dictates the frictional response. However, this contact stiffness is altered when a sensor is integrated into the system. This, often, is a case in LDCS. In LDCS, a known displacement/velocity is input, and the frictional force under these conditions is measured generally with the help of load cells. Load cell, when integrated into the system, changes the system's characteristics (stiffness, damping) and influences the contact stiffness of the tribo-system. This leads to a change in the nature of the asperity interactions resulting in a different frictional response as the contact conditions are no longer the same. In LFCS, the frictional force is not measured directly using force-measuring sensors. However, it is determined indirectly by calculating the acceleration/deceleration from the displacement response obtained using non-contact sensors. This eliminates the effect of sensor stiffness on the contact stiffness and results in asperity interactions closer to the actual conditions being simulated. This helps us calculate the accurate frictional force values closer to zero velocity in transient sliding conditions.
In the present work, two lateral force-controlled tribometers are designed. A parallel pendulum setup is designed to study the boundary lubrication regime of the Stribeck curve. A lateral force tribometer is designed to study the nature of friction between two surfaces subjected to suddenly applied forces.
The parallel pendulum tribometer is an energy-based tribometer designed to study the boundary lubrication regime of the Stribeck curve. This tribometer simulates the condition of combined rolling and sliding motion at the interfaces prevalent in many practical applications such as bearings, human body joints etc. The designed machine has high stiffness and is a highly under-damped system. Since the designed machine is a highly under-damped system, the energy input to the system is dissipated at much lower rates, resulting in many cycles of pendulum oscillations. As a result, we obtain many cycles/data points in the boundary lubrication regime of the Stribeck curve.
A lateral force tribometer is designed to conduct sliding experiments under tangential force-controlled transient conditions. These sliding conditions are prevalent in many tribo-systems, such as the seat belt-fabric tribo-system. The lateral force tribometer simulates the sliding conditions between two bodies in contact with each other when a sudden lateral force is applied to one body. Experiments are conducted using a seat belt-fabric, and a seat belt-polymer tribo-pair for different normal loads (in the range 10 N to 80 N) and three different initial tangential forces, 40 N, 60 N, and 80 N. Results show two regimes in the frictional response for different material pairs. The first region is the transient region in which there exists peak friction. This peak friction region is followed by a steady-state region in which constant friction is within the measured sliding distance. The occurrence of the peak friction and the value of the steady-state friction are found to be dependent on the contact stiffness of the interacting material pairs. This dependency of the CoF on the tangential contact stiffness is demonstrated by sliding experiments using stiffened fabric and steel-steel tribo-pairs
Numerical simulations of hydrogen flames in reheat gas turbine combustor: effect of pressure scaling and fuel blending
No full textWith a goal toward a net-zero energy supply, hydrogen, hydrogen-enriched natural gas, and biofuels, which reduce the carbon footprint, are actively being considered for firing stationary gas turbine engines. In this regard, the longitudinally-staged combustion concepts have been demonstrated to achieve low emissions and good fuel flexibility while operating over a wide range of load conditions. A particular implementation of such a concept is the constant pressure sequential combustor in Ansaldo Energia’s GT36 gas turbine comprised of two fuel stages implementing lean premixed combustion with different characteristics. In the first stage, the flame is stabilized aerodynamically and combustion occurs mainly by premixed flame propagation. The product gases from the first stage combustion are then blended with additional air in a dedicated mixer before entering the second stage combustor (also called the reheat burner) where additional fuel is added and combustion takes place at reheat conditions, i.e. it is controlled by spontaneous ignition due to the high temperature of the reactants. The reheat burner operation plays an important role in achieving the overall desired combustion characteristics. Recently, a high fidelity three-dimensional direct numerical simulation of the reheat flame with hydrogen fuel was performed to identify the modes of combustion and quantify their contributions towards fuel consumption at atmospheric conditions. However, the pressure in the practical system varies between 15 and 20 bar. The primary objective of this work is to understand the pressure scaling of flame in a reheat combustor using two-dimensional simulations. The computational domain consists of a mixing duct followed by a sudden expansion into a combustion chamber. A nine species, twenty-one reactions hydrogen-air mechanism is used for the detailed chemistry. Results show that at higher pressures the flame position is very sensitive to small perturbations in pressure/temperature, and can easily transition to an unstable state of combustion. Further, results on the flame structure and the role of auto-ignition will be presented. Chemical explosive mode analysis (CEMA) was used to qualify the fuel consumption rate between the auto-ignition and the flame propagation modes. With the increase in pressure, a significant decrease in fuel consumption due to auto-ignition was observed. To assess the effects of three-dimensional small-scale structures that are absent in two-dimensional simulations, a comparison of results between the two simulations was performed at atmospheric pressure. To understand the performance compromises observed in the hydrogen-rich regime of hydrogen-natural gas blends, further simulations with methane blended hydrogen were performed. Results illustrate a significant change in the flame stability and its structure. A detailed analysis of these results is also presented
Solid-state planar micro-supercapacitors: materials interfaces, state-of-art electrode design and self-powered device
No full textThe demand for miniaturization of energy storage systems has accelerated the development of on-chip micro-power devices for integration into portable electronic devices. Micro-supercapacitors can suitably cater to the need by functioning as efficient miniaturized energy storage devices with high power density, fast charge-discharge rates and long cyclic lifetime. The electrode material and its design are two dominant factors affecting the performance of a micro-supercapacitor. The thesis work focuses on fabrication of solid-state micro-supercapacitors using electrode design and material as the parameters to enhance the performance. The interfaces of materials were designed to attain pseudocapacitive properties for high electrochemical performance. Further, the strength of the electric field was improved through the rational design of electrodes utilized for the fabrication of micro-supercapacitors.
Solid-state micro-supercapacitor is presented with a planar sharp edge concentric circular geometry of gold electrode coated on a glass substrate and pseudocapacitive material for the charge storage. A few metal oxides and metal dichalcogenides such as ruthenium dioxide, manganese oxide (MnO), molybdenum disulphide (MoS2) are known to exhibit capacitive response similar to the carbon materials through a phenomena called pseudocapacitance. Thesis work uses key pseudocapacitive materials like iron (III) oxide (Fe2O3), MnO, and MoS2 in a matrix of electrically conducting carbon foam (CF) for solid-state micro-supercapacitor. Fe2O3 nanoparticles were directly synthesized on the walls of a three-dimensional (3D) CF matrix for high surface (209 m2/g) and enhanced pseudocapacitance. A systematic optimization was performed to achieve an optimal ratio of CF and Fe2O3 for a maximum enhancement of ~48% in charge storage capacity in a three-electrode electrochemical measurement. Polyvinyl alcohol–phosphoric acid was used solid and transparent electrolyte. The modified electrode design with ~23% larger perimeter and higher electric field at the tip of spikes (~68%) resulted in a high capacitance (~235%) compared with the conventional interdigitated electrodes. The device exhibited an excellent areal energy density (1.73 µWh/cm2) and cyclic stability (99.5% retention after 10000 cycles).
Asymmetric electrode configuration is used for a large potential window and hence, an increase in the energy density. All-pseudocapacitive asymmetric solid-state micro-supercapacitor was fabricated using MnO, which exhibits a potential window of -0.4 to 0.4 V in combination with Fe2O3 (a potential window of -1 to 0 V) along with CF matrix, where 3D CF-MnO and CF-Fe2O3 were used as anode and cathode materials, respectively. An elaborated optimization, provided a larger voltage window of 1.4 V with a high areal energy density of 5 µWh/cm2, which is 189% higher than that of CF-Fe2O3 for the planar electrode of micro-supercapacitor.
Metal dichalcogenides, recently have drawn a lot of attention due to the layered structure with high surface area and attributed to the charge transfer through Faradic reactions on the surface. MoS2 was combined with the CF matrix, where a significant contribution of charge storage was attributed to a diffusion-controlled mechanism (intercalated pseudocapacitance), elaborated using the Dunn’s method. In another electrode design, a novel zig-zag edge of the planar interdigitated electrodes was used to fabricate micro-supercapacitor. The design provided higher perimeter (~50% enhancement) and higher electric field (~57%) at each edge compared to the planar interdigitate electrodes. The solid-state micro-supercapacitors with novel zig-zag design exhibited a ~241% enhancement in capacitance compared with the planar edge electrode. The obtained result in modified design is higher than previously reported geometries introduced for better performance. Moreover, overall equivalent series resistance was lower by ~95% in the zig-zag edge electrodes than in planar edge electrodes, thus improving power capability. Furthermore, semiconducting MoS2, having an energy bandgap of 1.9 eV was utilized for the fabrication of an optically chargeable micro-supercapacitor under 600 nm illumination.
The optical interaction in optically chargeable micro-supercapacitor is further evaluated in a narrow bandgap material for infrared (IR) interaction. A novel pseudocapacitive, titanium sesquioxide (Ti2O3), a Mott-insulator with a bandgap of ~ 0.1 eV, was used as an electroactive material for device fabrication. In Ti2O3, the transition from semiconducting state to metallic state occurs after heating at 142 °C. Hence, pristine and annealed Ti2O3 (after ex-situ heating at 200 °C, 300 °C and 400 °C) was used in a symmetric configuration for the fabrication of planar micro-supercapacitor. Ti2O3-based solid-state micro-supercapacitors, annealed at 300 °C, showed a maximum enhancement in areal capacitance (~560%) compared to the pristine Ti2O3. The semiconducting to metallic states transition has a significant impact on the observed changes in the electrochemical response. A band merging is observed after annealing at a certain temperature, as obtained from the density functional theoretical calculation using temperature-dependent x-ray diffraction data of Ti2O3. The theoretical observation is in agreement with the obtained changes in electrochemical results observed because of annealing. The total charge storage due to different mechanisms in the Ti2O3 electrodes was quantitatively separated using Dunn’s method. Further, the optical interaction of Ti2O3 with IR exposure was exploited for the optically chargeable capability. The thesis work opens wider avenues to discover smart micro-supercapacitor designs for much-improved performance with added self-powering capability through combined optical and electrochemical interactions
Substrate interrogation of the CRISPR-Cas12a endonuclease reveals an unexpected functional plasticity
No full textSubstrate interrogation of the CRISPR-Cas12a endonuclease reveals an unexpected functional plasticity
Currently, Cas9 and Cas12a (also known as Cpf1) are the sole members of a large family of RNA-guided nucleases that have been widely used in genome manipulation and clinical interventions. Current studies on target discrimination by Cas9 and Cas12a nucleases are limited to single-stranded/double-stranded DNA, negatively supercoiled DNA and substrates with mismatch(es) between the RNA-guide and the DNA target-strand. However, much less is known about the full substrate landscape and biological functions of Cas12a nuclease. Knowledge on the mechanistic aspects of CRISPR-associated Cas nucleases is essential not only for genome engineering but also for reducing the risk off-target effects on the genome. Elucidation of substrate specificity of Cas12a would be important for understanding its role in bacterial immunity against invading bacteriophages and plasmids.
In this study, we report the characterization of guide-RNA independent binding and cleavage activity of CRISPR-AsCas12a using a variety of branched DNA structures. Purified AsCas12a was found to possess higher affinity towards various branched DNA substrates, as compared to single- and double strand DNA, without the participation of a divalent cation. Importantly, it showed highest binding affinity towards Holliday junction, among all the branched DNA species. In the presence of Mn2+ ion, Cas12a cleaved a variety of branched DNA substrates, including Holliday junction. Mapping of cleavage sites on a Holliday junction substrate revealed random, non-sequence specific mode of DNA cleavage. A glutaraldehyde crosslinking experiment suggests that Cas12a exists, and likely performs DNA binding and cleavage, as a monomer. A point mutation in its RuvC-like domain abrogated its cleavage function, but not DNA binding activity.
We found that AsCas12a binds to the crossover point and to each of the four arms of the HJ. This result is compatible with the findings that AsCas12a unwinds the HJ and non-specifically cleaves various branched DNA species in a RNA independent manner through a combination of endo- and exonuclease activities. In line with this, we observed that AsCas12a has an intrinsic RNA-independent, Mn2+-stimulated exonuclease activity that allows it to resect mononucleotides in the 5'-to- 3' direction. Furthermore, AsCas12a catalyses RNA-independent dsDNA cleavage (but not ssDNA) in the presence of Mn2+. Strikingly, AsCas12a variant harbouring a point mutation (D908A) in the RuvC-I domain and truncation variants lacking the RuvC-III domain or both RuvC-II and RuvC-III domains while retaining nearly the wild-type levels of HJ-binding activity showed reduced (△RuvC-III variant) and abrogation of (RuvC-ID908A and △RuvC-III+RuvC-II variants) DNA cleavage activities, respectively. An anti-CRISPR protein, AcrIIA4, inhibits the DNA cleavage activities of Cas12a on both unbranched and branched DNA substrates, but does not inhibit Cas12a-DNA complex formation. Altogether, these results uncover a broad range of DNA cleavage activities, which has implications in genome editing application and recognition of foreign DNA and cleavage
Provably Convergent Algorithms for Denoiser-Driven Image Regularization
No full textSome fundamental reconstruction tasks in image processing can be posed as an inverse problem
where we are required to invert a given forward model. For example, in deblurring and
superresolution, the ground-truth image needs to be estimated from blurred and low-resolution
images, whereas in CT and MR imaging, a high-resolution image must be reconstructed from
a few linear measurements. Such inverse problems are invariably ill-posed—they exhibit
non-unique solutions and the process of direct inversion is unstable. Some form of image
model (or prior) on the ground truth is required to regularize the inversion process. For
example, a classical solution involves minimizing f + g , where the loss term f is derived from
the forward model and the regularizer g is used to constrain the search space. The challenge
is to come up with a formula for g that can yield good image reconstructions. This has been
the center of research activity in image reconstruction for the last few decades.
“Regularization using denoising" is a recent breakthrough in which a powerful denoiser is
used for regularization purposes, instead of having to specify some hand-crafted g (but the
loss f is still used). This has been empirically shown to yield significantly better results than
staple f + g minimization. In fact, the results are generally comparable and often superior to
state-of-the-art deep learning methods. In this thesis, we consider two such popular models
for image regularization—Plug-and-Play (PnP) and Regularization by Denoising (RED). In
particular, we focus on the convergence aspect of these iterative algorithms which is not
well understood even for simple denoisers. This is important since the lack of convergence
guarantee can result in spurious reconstructions in imaging applications. The contributions
of the thesis in this regard are as follows.
PnP with linear denoisers: We show that for a class of non-symmetric linear denoisers
that includes kernel denoisers such as nonlocal means, one can associate a convex regularizer
g with the denoiser. More precisely, we show that any such linear denoiser can be expressed
as the proximal operator of a convex function, provided we work with a non-standard inner
product (instead of the Euclidean inner product). In particular, the regularizer is quadratic,
but unlike classical quadratic regularizers, the quadratic form is derived from the observed
data. A direct implication of this observation is that (a simple variant of) the PnP algorithm
based on this linear denoiser amounts to solving an optimization problem of the form f + g ,
though it was not originally conceived this way. Consequently, if f is convex, both objective
and iterate convergence are guaranteed for the PnP algorithm. Apart from the convergence
guarantee, we go on to show that this observation has algorithmic value as well. For example,
in the case of linear inverse problems such as superresolution, deblurring and inpainting
(where f is quadratic), we can reduce the problem of minimizing f + g to a linear system.
In particular, we show how using Krylov solvers we can solve this system efficiently in just
few iterations. Surprisingly, the reconstructions are found to be comparable with state-of-theart
deep learning methods. To the best of our knowledge, the possibility of achieving near
state-of-the-art image reconstructions using a linear solver has not been demonstrated before.
PnP and RED with learning-based denoisers: In general, state-of-the-art PnP and RED
algorithms rely on trained CNN denoisers such as DnCNN. Unlike linear denoisers, it is
difficult to place PnP and RED algorithms within an optimization framework in the case of
CNN denoisers. Nonetheless, we can still try to understand the convergence of the sequence
of iterates generated by these algorithms. For convex loss f , we show that this question can be
resolved using the theory of monotone operators — the denoiser being averaged (a subclass of
nonexpansive operators) is sufficient for iterate convergence of PnP and RED. Using numerical
examples, we show that existing CNN denoisers are not nonexpansive and can cause PnP
and RED algorithms to diverge. Can we train denoisers that are provably nonexpansive?
Unfortunately, this is computationally challenging—simply checking nonexpansivity of a
CNN is known to be intractable. As a result, existing algorithms for training nonexpansive
CNNs either cannot guarantee nonexpansivity or are computation intensive. We show that
this problem can be solved by moving away from CNN denoisers to unfolded deep denoisers.
In particular, we are able to construct unfolded networks that are efficiently trainable and
come with convergence guarantees for PnP and RED algorithms, and whose regularization
capacity can be matched withCNNdenoisers. Presumably, we are the first to propose a simple
framework for training provably averaged (contractive) denoisers using unfolding networks.
We provide numerical results to validate our theoretical results and compare our algorithms
with state-of-the-art regularization techniques. We also point out some future research
directions stemming from the thesis
Dynamics of Quantum Supercooled Liquids: A Mode Coupling Approach
No full textIn this thesis, I use the quantum mode coupling theory (QMCT) formulation to
study the dynamics in a supercooled liquid to understand how quantum fluctuations affect the liquid-glass transition. I calculate the Kubo-transformed density
correlation function in order to avoid the difficulties associated with the direct
calculation of the quantum correlation functions. The Kubo and the quantum
correlation functions are connected through a mapping of quantum particles
into classical ring-polymers. The radius of gyration of the polymer is directly
related to the uncertainty in the position of the quantum particle. The position
uncertainty increases with the quantumness of the system, which is quantified
in terms of the thermal de-Broglie wavelength.
I propose a perturbative method to simplify the form of the self-consistent
equations of QMCT, which makes it feasible to study the relaxation dynamics
directly in the time-domain, significantly reducing the computational cost. Implementing the perturbative calculation in the hard-sphere supercooled liquid,
I find that moderate quantum fluctuations can cause enhanced caging, leading
to liquid-glass transition at densities smaller than the classical transition density.
The relaxation time associated with the density fluctuations shows power-law
divergence with increasing density, similar to the classical HS system. However,
the power-law exponents show a linear rise with increasing quantum fluctuations, which suggests a dynamic nature of the quantum effect. Further, at a
fixed density, far from transition point, relaxation time shows an exponential
(Vogel-Fulcher-Tamman) increase with the quantum fluctuation, which crosses
over to a power-law like divergence as the transition point is approached.
Extending the study to higher quantum regime, I observe that an enhanced
tunneling effect leads to a re-entrant transition from glass to liquid phase. The
intervening glass phase allows us to divide the liquid phase into two: low and
xii
high quantum liquids. The relaxation time in the high quantum regime shows a
power-law like divergence as the liquid-glass transition point is approached. The
study shows faster relaxation in the higher quantum regime due to enhanced
tunneling.
I further analyze the frequency-dependent specific heat in the supercooled
quantum liquid. Liquid-glass transition is generally thought of as a second order
phase transition; thus specific heat measurement is one of the important tools
to detect it. I use QMCT and Zwanzig’s formalism to express specific heat in
terms of the longitudinal viscosity of the liquid. I find a substantial variation
in frequency-dependence of the specific heat as the quantumness of the liquid
is changed, and this variation becomes more significant as the density of the
system is increased. Near the glass transition point, slower dynamical modes
contribute to the specific heat in quantum liquids as compared to the classical
liquids.
Another fundamental observable to analyze relaxation processes in liquids
is the tagged-particle dynamics. The tagged-particle density correlation acts
as the generating function of the moments of tagged-particle displacement. I
derive a coupled set of equations for the second and the fourth moments (Kubotransformed) of tagged-particle displacement using QMCT. The most interesting
results for these moments are obtained in the short times which are related to
the uncertainty due to quantum fluctuation. The non-zero values of the moments at zero-time due to quantum uncertainty stands out from the classical
case. The non-Gaussian nature of the particle distribution function at short (ballistic) times leading to strong dynamical heterogeneity in the tagged-particle
motion further reflects the enhanced quantum effect. I derive an analytic expression for diffusion coefficient which shows non-monotonous behavior with
increasing quantumness and qualitatively reflects the re-entrant diffusive behavior observed in Lennard-Jones simulations.UGC, IIS
Analysis of Residual Estimate of Local Truncation Error
No full textThis thesis focuses on understanding the behaviour of the residual error estimator, referred to as R- parameter, in the context of Finite Volume Method. R-parameter measures the local truncation error (LTE) which is generated locally in each cell due to spatial and temporal discretization. Even though there are numerous applications of R-parameter, it is also sensitive to various parameters. The sensitivities associated to R-parameter are studied through numerical experiments and theoretical analysis. For this, steady circular convection and scalar convection-diffusion problems are considered.
The different gradient-finding methods employed for evaluating LTE can influence the R-parameter. The accuracy of these methodologies is studied empirically using 2D test function. Consistent to finite volume method, the cell-averaged values are used for accuracy studies.
The comparison of error fall rates and error levels obtained from different variants of error estimators are discussed in detail. We have also proposed a simple method based on generalized finite difference for determining the residual, which shows a lot of promise owing to the simplicity of its implementation.
Patch analysis is performed to establish the relevance of the procedures analysed to AMR. In order to understand the correctness of the estimated errors, the qualitative and quantitative analysis of the local error distribution over the whole domain are carried out for scalar convection problem. This work also establishes the suitability of QLS based error estimator to determine errors associated with a viscous flux discretization
Analysis and Methods for Knowledge Graph Embeddings
No full textKnowledge Graphs (KGs) are multi-relational graphs where nodes represent entities, and typed edges represent relationships among entities. These graphs store real-world facts such as (Lionel Messi, plays-for-team, Barcelona) as edges, called triples. KGs such as NELL, YAGO, Freebase, and WikiData have been very popular and support many applications such as Web Search, Query Recommendation, and Question Answering. Although popular, these KGs suffer from incompleteness. Learning Knowledge Graph Embeddings (KGE) is a common approach for predicting missing edges (i.e., link prediction) and representing entities and relations in downstream tasks. While numerous KGE methods have been proposed in the past decade, our understanding and analysis of such embeddings have been limited. Further, such methods only work well with ontological KGs. In this thesis, we address these gaps.
Firstly, we study various KGE methods and present an extensive analysis of these methods, resulting in many insights. Next, we address an under-explored problem of link prediction in Open Knowledge Graphs (OpenKGs) and present a novel approach that improves the type compatibility of predicted edges. Lastly, we present an adaptive interaction framework for learning KG embeddings that generalizes many existing methods.
In the first part, we present a macro and a micro analysis of embeddings learned by various KGE methods. Despite the popularity and effectiveness of KG embeddings, their geometric understanding (i.e., arrangement of entity and relation vectors in vector space) is unexplored. We initiate a study to analyze the geometry of KG embeddings and correlate it with task performance and other hyper-parameters. Firstly, we present a set of metrics (e.g., Conicity, ATM) to analyze the geometry of a group of vectors. Using these metrics, we find sharp differences between the geometry of embeddings learned by different classes of KGE methods. The vectors learned by a multiplicative model lie in a narrow cone, unlike additive models where the vectors are spread out in the space. This behavior of multiplicative models is amplified by increasing the number of negative samples used for training. Further, a very high Conicity value is negatively correlated with the performance on the link prediction task. We also study the problem of understanding KG embeddings’ semantics and propose an approach to learn more coherent dimensions. A dimension is coherent if the top entities have similar types (e.g., person). In this work, we formalize the notion of coherence using entity co-occurrence statistics and propose a regularizer term that maximizes coherence while learning KG embeddings. The proposed approach significantly improves coherence while having a comparable performance with baseline in the link prediction and triple classification tasks. Further, based on the human evaluation, we demonstrate that the proposed approach learns more coherent dimensions than the baseline.
In the second part, we address the problem of learning KG embeddings for Open Knowledge Graphs (OpenKGs), focusing on improving link prediction. An OpenKG refers to a set of (head noun phrase, relation phrase, tail noun phrase) triples such as (tesla, return to, new york) extracted from a text corpus using OpenIE tools. While OpenKGs are easy to bootstrap for a domain, they are very sparse. Therefore, link prediction becomes an important step while using these graphs in downstream tasks. Learning OpenKG embeddings is one approach for link prediction that has received some attention lately. However, on careful examination, we find that current algorithms often predict noun phrases (NPs) with incompatible types for given noun and relation phrases. We address this problem and propose OKGIT that improves OpenKG link prediction using novel type compatibility score and type regularization. With extensive experiments on multiple datasets, we show that the proposed method achieves state-of-the-art performance while producing type compatible NPs in the link prediction task.
In the third part, we address the problem of improving the KGE models. Firstly, we show that the performance of existing approaches vary across different datasets, and a simple neural network-based method can consistently achieve better performance on these datasets. Upon analysis, we find that KGE models depend on fixed sets of interactions among the dimensions of entity and relation vectors. Therefore, we investigate ways to learn such interactions automatically during training. We propose an adaptive interaction framework for learning KG embeddings, which can learn appropriate interactions while training. We show that some of the existing models could be seen as special cases of the proposed framework. Based on this framework, we also present two new models, which outperform the baseline models on the link prediction task. Further analysis demonstrates that the proposed approach can adapt to different datasets by learning appropriate interactions