Indian Institute of Science Bangalore
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On some canonical metrics on holomorphic vector bundles over Kahler manifolds
No full textThis thesis consists of two parts. In the first part, we introduce coupled Kähler-
Einstein and Hermitian-Yang-Mills equations. It is shown that these equations have
an interpretation in terms of a moment map. We identify a Futaki-type invariant as an
obstruction to the existence of solutions of these equations. We also prove a Matsushima-
Lichnerowicz-type theorem as another obstruction. Using the Calabi ansatz, we produce
nontrivial examples of solutions of these equations on some projective bundles. Another
class of nontrivial examples is produced using deformation. In the second part, we prove
a priori estimates for vortex-type equations. We then apply these a priori estimates
in some situations. One important application is the existence and uniqueness result
concerning solutions of the Calabi-Yang-Mills equations. We recover a priori estimates
of the J-vortex equation and the Monge-Ampère vortex equation. We establish a corre-
spondence result between Gieseker stability and the existence of almost Hermitian-Yang-
Mills metric in a particular case. We also investigate the Kählerity of the symplectic form
which arises in the moment map interpretation of the Calabi-Yang-Mills equations
Response of Granular Materials Towards Blast Loading
No full textGranular media, such as sand, soil, and rocks, are commonly encountered in various engineering
and geotechnical applications, and their response to blast loading is of significant interest. In this
master’s thesis, the attenuation characteristics and equation of state of granular media subjected
to different blast wave loadings are investigated.
Experimental investigations are conducted to determine the attenuation characteristics of
granular media subjected to blast loading. A series of laboratory-scale experiments are performed
using a shock tube apparatus to generate controlled blast waves. Granular media samples of
different types (naturally available sand and artificially generated glass beads) are subjected to
different blast wave loadings. The response of the granular media, including the transmitted
pressure and impulse, is measured using pressure sensors. The experimental results are analyzed
to determine the attenuation characteristics of the granular media, including the attenuation
coefficient, the influence of blast wave parameters and packing density of the granular media on
the attenuation. It was discovered that the extent of attenuation was higher when blast waves
impinged on sand samples with 43 % relative density compared to the scenario when the sand
samples were packed to 25 % relative density. The range of attenuation coefficient is (-4.70 to
-7.48) for 25% relative density sand samples and for experiments done on 43% relative density
sand samples it was found to be in the range (-5.12 to -8.88).
Furthermore, experiments have been conducted to come up with equation of state (EOS)
to describe the behavior of granular media under blast loading. The EOS relates the change
in granular media properties, such as particle velocity, to the applied blast wave loading. The
parameters of the EOS are determined using the experimental data obtained from the high-speed imaging experiments. Relationship among particle velocity UP , wave speed US and pressure P
described by following equations together is a basic equation of state for sand compacted till 43
% relative density as the granular media when subjected to blast loading of varying intensities.
The findings of this research contribute to a better understanding of the response of granular
media to blast loading and provide valuable insights for engineering and geotechnical applications
where granular media are subjected to blast loads. The results also highlight the importance of
blast wave characteristics and granular media properties in determining the attenuation behavior
and equation of state of granular media under blast loading. Further research opportunities
are identified, including the validation of the EOS using field-scale experiments and numerical
simulations
A stable Strontium isotopic (δ88/86Sr) study of seawater from the Bay of Bengal, coastal groundwater from the Bengal Basin, and the Ganges, Brahmaputra, Mahanadi, and Godavari rivers in India
No full textStrontium (Sr) is an alkaline earth element that has four naturally occurring stable isotopes, 84Sr, 86Sr, 87Sr and 88Sr. During measurements of the radiogenic Sr isotope ratio (87Sr/86Sr), which is a widely used tracer in Earth sciences, the instrumental mass dependent fractionation is corrected by assuming the 88Sr/86Sr ratio as 8.375209. However, with the recent advancements in mass spectrometry, it is now possible to resolve variations in the 88Sr/86Sr ratio (expressed as δ88/86Sr) in natural samples. In this study, a measurement protocol for stable Sr isotope ratio measurements was developed using a double spike thermal ionization mass spectrometry (DS-TIMS) technique and δ88/86Sr variability in depth-bound seawater, groundwater, and large rivers are investigated.
The analytical technique for high precision TIMS measurements of δ88/86Sr was developed using a new Sr double spike (87Sr-84Sr); the single spikes used to prepare this double spike were less pure compared to the spikes reported in literature and hence the DS of this study is less expensive and differs in isotopic composition from DS used in previous studies. The robustness of the method was validated by measurements of multiple standards of different matrices (carbonate, silicate, seawater, and pure Sr) and the long-term external reproducibility of δ88/86Sr was less than ± 0.035 ‰ (2SD) which is comparable to, if not better than previous studies. The δ88/86Sr values are not affected by the nature of the loading filament (tantalum versus zone refined rhenium) or amount of Sr loaded on the filament; further, the δ88/86Sr values are invariant over a wide range of spike/sample ratios, consistent with modelling calculations for error propagations. The δ88/86Sr values, relative to the NIST SRM987 standard, are reported for an Alfa Aesar ICPMS Sr standard (0.101 ± 0.033 ‰), NASS-6 seawater (0.387 ± 0.034 ‰), JCp-1 coral carbonate (0.196 ± 0.006 ‰), JCt-1 clam shell (0.252 ± 0.004 ‰), BCR-2 basalt (0.264 ± 0.003 ‰), and NIST SRM987 (0 ± 0.023 ‰).
The Bay of Bengal, which has crucial control on marine Sr budget, receives large influx of continental Sr through the Himalayan rivers in form of surface flow with additional contribution from groundwater discharge. The present study reports restricted variability in the δ88/86Sr values (0.373-0.411 ‰) of seawater samples collected from multiple depths (0-1500 m) in the Bay of Bengal with an average δ88/86Sr = 0.388 ± 0.025 ‰ (2SD), which overlaps with previous estimates of global seawater.
The chemistry of coastal seawater can be significantly influenced by groundwater and interactions between Bengal Basin groundwater and the adjacent Bay of Bengal seawater are well documented. This thesis presents δ88/86Sr values, 87Sr/86Sr, as well as stable Ca isotope (δ44/40Ca) data for a set of groundwater samples collected from multiple depths (14-333 mbgl) from coastal aquifers in and around the Sundarbans delta, India. Significant variabilities were observed in 87Sr/86Sr, salinity, and cation concentrations across depths which indicate seawater incursion at shallower depths (14-42 mbgl) while deep aquifer samples (~333 mbgl) retained freshwater signature. A substantial variability in δ88/86Sr values (~0.542 ‰) was observed in these groundwater samples with shallow aquifer samples showing high δ88/86Sr (up to 0.666 ‰), which is higher than modern seawater (~0.388 ‰). These variations along with modelling results suggest appreciable amounts of precipitation of secondary carbonates in the saline groundwaters along with indications of seawater-freshwater mixing. The δ44/40Ca values of the same samples show similar trends as the δ88/86Sr values and are consistent with removal of solute Ca as aragonites or calcites (up to 45%).
Rivers are major transport pathways of weathering-derived continental Sr to the oceans and play a major role in modulating the overall Sr budget among modern reservoirs. The δ88/86Sr values in seasonally and spatially resolved river water samples from the lower Ganges (Hooghly River) varied from -0.167 to 0.418 ‰ while those in seasonally distributed river water samples from the Brahmaputra, collected from Guwahati and Jorhat, range between 0.136-0.304 ‰. Spatially and seasonally resolved river water from the Mahanadi Basin display δ88/86Sr values between 0.263-0.638 ‰; few samples from coastal regions overlapped with Bay of Bengal δ88/86Sr values underscoring seawater intrusion. The Mahanadi Basin groundwater samples display δ88/86Sr values between 0.276-0.423 ‰, which overlap with compositions of the Mahanadi River water, consistent with riverwater-groundwater interactions. Seasonally resolved river water samples from the Godavari River, collected from Rajahmundry, showed δ88/86Sr variability between 0.174-0.640 ‰. Overall, the significant variability in δ88/86Sr values of these large rivers broadly overlap with global river water data and reflect varying sources, congruent versus incongruent chemical weathering, with implications for role of water mass mixing and secondary minerals, such as carbonates and clays in river waters
Effect of Processing Mg-6zn-0.2ce Through High-pressure Torsion on Its Use as a Biomaterial
No full textHere, we investigate the effect of high-pressure torsion (HPT), a severe plastic deformation process, on the mechanical properties, corrosion, and cytotoxicity of Mg-6Zn-0.2Ce alloy, a candidate material for bioresorbable bone implants. This alloy was processed by quasi-constrained HPT by applying a pressure of 6 GPa at room temperature for 1, 2, and 5 turns. Samples processed to two turns of HPT showed the smallest grain size, the highest strength that was approximately five times higher than the as-received coarse-grained sample and a reduction in the ductility. Electrochemical impedance spectroscopy and potentiodynamic polarization demonstrated the highest corrosion resistance for the Mg-alloy processed for two turns of HPT; however, accelerated degradation due to pitting corrosion was observed after immersion in simulated body fluid (SBF) for three days. Nevertheless, all HPT-processed samples showed lower corrosion rates in all corrosion tests compared to their annealed counterparts. Finally, cell culture revealed good cytocompatibility without any noticeable changes in cytotoxicity following HPT processing. Overall, HPT for two turns showed enhanced strength and reduced corrosion rates without loss in cytocompatibility for the Mg-6Zn-0.2Ce alloy, making it a promising strategy to enhance the performance of the alloy as a bioresorbable orthopedic biomaterial. This work highlights the potential of HPT as a viable technique to improve the biomedical performance of Mg alloys for engineering next-generation biomedical implants
Exploring End-of-Life Photovoltaic (PV) Panel as a Building Material: A Case of Crystalline Silicon PV
No full textThe renewable energy share in the energy mix worldwide is rising sharply to mitigate
climate change, with Solar Photovoltaics (PV) carrying a large share of 3.6%. However,
the end-of-life (EoL) management of decommissioned PV panels is emerging as a serious
concern, globally. It is projected that by the end of 2050, a cumulative 70~80 million tonnes
of EoL-PV waste will be generated worldwide, with 4.5~7.5 million tonnes envisaged in India.
Such enormous PV waste heading into landfills severely threatens the environment and
human health. The current study explores a novel, hitherto untried, approach of upcycling
EoL-PV panels as a building material. EoL-PV also carries potential for application in housing,
alleviating the pressure on conventional building materials. Further, upcycling PV panels could
extend the use-phase by a few decades, buying time till recovery and recycling options
become economically viable.
For application as a building material, EoL-PV panels need to be examined for their solar and
thermal transmittance. PV panels, before they reach end of functional life (EoL), undergo
degradation subject to various field (environmental) and operating conditions. The impact of
degradation on the solar and thermal transmittance of EoL-PV panels has not been examined
thus far. About 33 decommissioned EoL-PV panels with various degradation modes have been
visually and electrically examined along with 2 new(unused) PV panels. EoL-PV panels are
non-opaque materials, and hence solar transmittance measurements could provide crucial
insight into their climatic performance. Further, the impact of degradation on solar and
thermal transmittance has been examined, comparing EoL-PV panels and new (unused) PV
panels. The measurement approach adopted (under natural sunlight) has been a maiden
attempt in examining PV panels. ASTM E1084-86:2015 stipulations for such measurements
have been complied with. Compared with new PV panels, a drop in solar transmittance of 11
% ~ 37.6 % has been observed in EoL-PV panels. Both EoL-PV and new PV panels have also
been tested for their thermal transmittance in a state-of-the-art HotBox facility. No significant
changes between EoL-PV and new PV in their thermal transmittance were observed. The
absolute U-values were in the range of 11.7 W/m2
K ~ 12.5 W/m2
K, with their thermal
conductivity in the range of 0.55 ~ 0.7 W/mK.
The climate responsiveness on EoL-PV building has been examined for various climate zones
in India. This has involved a real-time monitoring of a case study building (building integrated
with EoL-PV as façade), supported by whole-building simulation models. Time lag and
decrement factors are parameters to examine the climatic response of a building envelope.
The time lag for the EoL-PV case was observed to be very low (< 1 hour), and the decrement
factor around 1. The thermal damping was found to be negative, indicating that the indoor
air temperature is higher than outdoor ambient temperatures. For tropical conditions such as
India, this would imply a large heat gain, which is not favourable. Suitable interventions need
to be devised to improve the thermal performance of the EoL-PV envelope. Four interventions
have been proposed and tested through whole building simulations. Significant improvement
in the decrement factor (0.4 ~ 0.7) and time lag (6~8 hrs) have been achieved for favourable
adoption in tropical conditions.
Given the huge demand in housing, the current study has examined the applicability of EoL PV for housing and in alleviating the demand for conventional building materials.
Conventional building materials are energy intensive and carry a huge carbon footprint. There
is an emerging paradigm shift in the adoption of novel building materials with low embodied
energy. EoL-PV is an affordable and durable material with an inherent low embodied energy.
From a sustainability perspective, the current study also examines the energy, cost and
carbon-emission benefits accruing through the adoption of EoL-PV buildings in comparison
with conventional buildings. EoL-PV panels carry inconsistent degradation, which depends on
the age of PV, climate zone and other factors. An approach has been developed to determine
the probability of degradation modes for a given climate zone, including the impact of
climate-change. Based on this, state-wise projections on the number of EoL-PV panels likely
to be generated in India, and the minimum number of houses adopting EoL-PV has been
estimated as part of this study.
The result from the study strongly favours the application of EoL-PV as a building material
with appropriate interventions customised to achieve indoor thermal comfort in response to
the prevalent climatic conditions. This makes EoL-PV a valuable decentralized resource with
potential to support Net-zero building
Insights into evaporation, atomization and precipitate formation of polymer droplets
No full textEvaporation of polymer droplets is an active area of interest due to its applications in systems such as ink jet printing, thin films, spray combustors to name a few. Thus, understanding complex dynamics of evaporating polymer droplets in different experimental configurations is crucial to cater to the wider industrial applications. This study investigates evaporation and subsequent dynamics of two classes of polymeric droplets-low viscoelastic (PAM) and high viscoelastic (PEO) in two different experimental configurations: Laser induced evaporation of droplet under acoustic levitation, natural evaporation of droplet on hydrophobic surfaces.
In the first part, we investigate the interaction of an aqueous low viscoelastic polymer droplet (PAM) with a tunable continuous laser in an acoustically levitated environment. Depending on the laser irradiation intensity and polymer concentration, we observe four temporal phases: droplet evaporation, vapor bubble growth followed by membrane inflation, bubble/membrane rupture through hole nucleation, and droplet breakup. During the initial droplet evaporation phase, concentration build-up at the droplet surface beyond a critical limit lead to the formation of a skin layer. It is revealed that at a given location inside the droplet, hot spots occur, and the maximum temperature at the hot spots scales linearly with irradiation intensity until a bubble nucleates. The low-intensity laser interaction leads to symmetric membrane inflation that eventually forms holes at droplet poles and cracks on the shell surface. On the contrary, high intensity causes early bubble nucleation followed by asymmetric membrane inflation that eventually ruptures through multiple hole formation. Furthermore, the growth and rupture of the membrane is followed by a catastrophic breakup of the droplet. Two dominant atomization modes are reported at significantly high irradiation intensities: stable sheet collapse and unstable sheet breakup. The evolution of droplets into a stable/unstable sheet follows universally observed ligament and hole dynamics. A regime map is shown to describe the influence of polymer concentration and irradiation intensity on the strength and mode of droplet atomization.
In the second part, we investigate the interaction of a aqueous high viscoelastic polymer droplet (PEO) with a tunable continuous laser in an acoustically levitated environment. Depending on the laser irradiation intensity, we observe nucleation of a bubble in the dilute regime of polymer concentration, contrary to the previously observed bubble nucleation in a semi-dilute entangled regime for low viscoelastic modulus polymer droplets. After the bubble nucleation, a quasi-steady bubble growth occurs depending on the laser irradiation intensity and concentrations.
Our scaling analysis reveals that bubble growth follows Plesset-Zwick criteria independent of the viscoelastic properties of the polymer solution. Further, we establish that the onset of bubble growth has an inverse nonlinear dependence on the laser irradiation intensity. At high concentrations and laser irradiation intensities, we report the expansion and collapse of polymer membrane without rupture, indicating the formation of an interfacial skin with significant strength. The droplet oscillations are primarily driven by the presence of multiple bubbles and, to some extent, by the rotational motion of the droplet. Finally, depending on the nature of bubble growth, different types of precipitate form contrary to the different modes of atomization observed in low viscoelastic modulus polymer droplets.
In the third part, we experimentally report the concentration and molecular weight dependence of the deposit patterns of low viscoelastic evaporating polyacrylamide (PAM) droplets on hydrophobic surfaces. We find that with an increase in non-dimensional concentrations c⁄c^* ranging from 0.16 (dilute) to 66.66 (semi-dilute entangled) there is a gradual transition from ring to uniform precipitates. However, with a decrease in the molecular weight of the polymer by one order, the coffee ring formation was not suppressed for the reported range of concentration. We attribute these results to the role played by the critical overlap concentration (c^*) and diffusion coefficient of polymer along with the evaporation modes.
Lastly, the authors report the experiments on the precipitate formation of evaporating (PEO) droplets on hydrophobic surfaces. We observe the final precipitates to be deformed with the formation of central dip over the concentrations ranging from semi-dilute unentangled to semi-dilute entangled.
Overall, this study provides valuable insights into the complex phenomenon of evaporation of polymer droplets in different configurations and its importance in various industrial and natural processes. The findings can help optimize these processes and improve our understanding of them
Stochastic Finite Element Modeling of Material and Geometric Uncertainties in Electromagnetics
No full textDesign methodologies for RF/Microwave systems require major changes to cope up with the evolution of faster, high data/rate wireless communication systems using 5G and futuristic 6G technologies. The research on Terahertz communication and imaging has gained the interest of electromagnetics (EM) community.
Robust design of these components incorporating manufacturing process tolerances would enhance the fabrication yield and thereby reduce the overall production cost. Estimating these effects in the design phase is ideal, but the limitations of analytical methods both in EM and stochastic analysis call for numerical estimation of such uncertainties. Similar uncertainties are also encountered in the analysis of electromagnetic field interaction with biological samples as the EM properties of these samples may change with physiological or diurnal variations. Most popular computational electromagnetics (CEM) algorithms are deterministic and the impact of uncertainties such as these random variations in properties of the media or geometric variations is usually ignored due to the high computational time.
This thesis develops efficient computational methods to estimate these stochastic variations using a spectral representation of these randomly varying parameters. First, a computational framework for analyzing variations in the dielectric constant of a region in an EM model is represented using random variables. The resultant electric field becomes a random field which is represented using polynomial chaos expansion (PCE). This representation has been extended further to develop algorithms for stochastic variation in multiple subdomains.
The above random variable representation alone is insufficient when the material has spatial variations. Karhunen-Loève expansion (KLE) is used for representing these input variations with minimum stochastic dimension. KLE can be truncated at the desired accuracy level to obtain the stochastic response to the spatial variation of material properties. As KLE-SSFEM is extended to multiple subdomains the stochastic dimension may increase. Even though the scheme has a sparse matrix, its size may cross the capability of computers. To tackle this situation, a spatially averaged SSFEM (SA-SSFEM) is developed which limits the stochastic dimension to the number of stochastic subregions. This enables the stochastic analysis of large EM models using spectral stochastic FEM.
Simulation outcomes like, transmission coefficient and reflection coefficient are analyzed to obtain their probability density estimation due to variation in permittivity and loss tangent in discrete dielectric sections inside a waveguide. The stochastic characterization of resonance frequency and transmission coefficients of a dielectric loaded microstrip line is also estimated where the dielectric properties of a pellet are allowed to be stochastic and spatially varying. These numerical results are found to match the Monte Carlo simulation (MCS) with 10,000 samples. Probability density function (PDF) obtained from the proposed method is systematically compared MCS by performing two variable KS-test.
Based on the success of above method for analyzing material variations, a novel geometrical SSFEM (GSSFEM) is proposed to analyze dimensional uncertainty in 3-D microwave models. The most challenging part in the stochastic analysis of geometric variation in finite element model is handling of mesh modifications in an intrusive framework. Therefore, currently only non-intrusive methods which require re-meshing of the physical model in every sample execution, are employed for such analyses. On the other hand, this is handled in the proposed GSSFEM by using Piola transformation where the mesh movement in tetrahedral elements are captured to a reference element. The Jacobian of an element used for Piola mapping is represented as a function of stochastic variables to capture mesh level uncertainties. Polynomial chaos expansion is used for approximating the electric field as a random process. This is the first such formulation of geometric uncertainties in a full-wave 3-D model, using an intrusive approach. The proposed technique is validated by applying it to waveguide devices with uncertainty in geometric dimensions and the results are compared with the Monte Carlo simulations. The proposed scheme is faster than sparse grid stochastic collocation, even with the computational scaling for the same degrees of freedom and stochastic dimension.
The above finite-element based stochastic formulations for electromagnetics employ edge elements and the resulting mathematical models result in sparse matrices thereby resulting in computationally efficient schemes. These stochastic methods can be employed by designers for analyzing the impact of fabrication tolerance of passive components at microwave frequencies and beyond
Algortihms for Individual and Collective Fairness Measures
No full textThe problem of fair allocation has been a central topic in economic theory, and the literature on fair division has provided fundamental insights on how to allocate resources among agents in a fair manner. By drawing upon existing literature, this thesis focuses on computational challenges that arise in different settings of fair-division problems. The thesis presents efficient algorithms, including approximation algorithms where applicable, for fair resource allocation by optimizing for different types of fairness measures. We also complement these algorithms by providing matching hardness results demonstrating the tightness of the obtained approximation guarantees. This thesis is structured into two parts, based on the criteria for measuring fairness: collective and individual.
Part-I: Collective Fairness
Algorithms for maximizing p-mean welfare
The first contribution of this thesis is a polynomial-time algorithm for allocating indivisible goods among agents with subadditive valuations. We consider p-mean welfare objectives, that encompasses a range of welfare functions, including utilitarian social welfare, Nash social welfare, and egalitarian welfare. Our algorithm achieves an 8n-approximation ratio for the Nash social welfare objective, which is a significant improvement over the previously known approximation ratio of O(n log n). Moreover, for any given p, our algorithm computes an allocation with p-mean welfare at least 1 times the optimal. Our results hold for the wide range of subadditive valuations, including XOS and submodular valuations. We also show that our approximation guarantees are essentially tight for XOS valuations.
Maximizing Nash social welfare for fair coverage
The second contribution of this thesis is a polynomial-time algorithm for maximizing Nash social welfare in coverage problems. We consider the problem of selecting T subsets of agents that achieve fair and efficient coverage while satisfying combinatorial constraints. We propose a valuation function based on the number of subsets that contain each agent, and design an algorithm that achieves an (18 + o(1))-approximation ratio for maximizing Nash social welfare in coverage instances. Our algorithm applies to instances where an FPTAS for weight maximization exists, and we complement our algorithmic result by proving that Nash social welfare maximization is APX-hard in coverage instances.
Part-II: Individual Fairness
Fair division using subsidy under dichotomous valuations
The third contribution of this thesis is a subsidy-based algorithm for achieving envy- freeness in the allocation of indivisible goods among agents with dichotomous valuations. We show that it is possible to allocate goods among agents with dichotomous valuations in an envy-free manner with a per-agent subsidy of either 0 or 1, and such an envy-free solution can be computed efficiently in the standard value-oracle model. Our results hold for general dichotomous valuations, including non-additive and non-submodular valuations, and our subsidy bounds are tight, providing a linear improvement over the bounds known for general monotone valuations.
The results presented in this thesis provide new tools to address fair allocation problems in practice and offer insights into the design of efficient procedures for fair resource allocation
Search for dark matter produced in association with a Higgs boson decaying to a pair of bottom quarks in proton-proton collisions at √s= 13 TeV using CMS 2017 and 2018 data
No full textThe discovery of the Higgs boson has opened a new portal to search for
Dark Matter(DM). Since DM does not interact in the CMS detector, searches
rely on the missing transverse energy in association with a visible SM particle. The final state of the Higgs boson+missing transverse energy is known as ”mono-Higgs”. In this thesis, mono-Higgs analysis has been performed in two categories; Boosted and Resolved.
In the first part of the thesis, we present a search for DM when it is produced
in association with a highly boosted Higgs boson decaying to a pair of bottom
quarks using data collected at CMS detector in 2017 and 2018, corresponding
to a total luminosity of 101.3 fb-1. The Higgs boson is reconstructed using a
fatjet (AK8jet), and it decays to bb quarks is identified using the DeepDoubleB tagger algorithm. This category targets the phase space where the DM-SM mediator mass is high. Two sensitive observables, missing energy and mass of the Higgs boson, are used for this search. Finally, we compare observed and expected events and interpret results in terms of the upper limit in the context of three signal models: 2HDM+a, Z’-2HDM and Baryonic-Z’.
In the second part of the thesis, we present a search for DM when it is
produced in association with a low or medium-boosted Higgs boson decaying
to a pair of bottom quarks using data collected at CMS detector in 2017 and
2018 corresponding to a total luminosity of 101.3 fb-1. Higgs boson is reconstructed
using two narrow jets (AK4jets), and deepCSV algorithm is used to identify b quarks. This category targets the phase space where DM-SM mediator mass is low. The observables of missing energy and mass of the Higgs boson are used for this search. Results are interpreted in terms of the upper limit in the context of three signal models: 2HDM+a, Z’-2HDM and Baryonic-Z’.
Finally, we present the combination of resolved and boosted categories results
for all three models and show a projection of this search for Run3 and HL-LHC
in the context of 2HDM+a model
Algorithms for Geometric Packing and Covering Problems
No full textWe study two fundamental problems related to geometric packing and covering, and design
algorithms with improved worst-case performance guarantees for them. These problems have
numerous applications in resource allocation, logistics, packing, and sensor networks.
First, we study the Strip Packing problem (SP), where we are given a vertical half-strip
\left[0,W\right]\times\left[0,\infty\right) and a set of n axis-aligned rectangles of width at most W . The goal is to find
a non-overlapping packing of all rectangles into the strip such that the height of the packing
is minimized. A well-studied and frequently used practical constraint is to allow only those
packings that are guillotine separable, i.e., every rectangle in the packing can be obtained
by recursively applying a sequence of edge-to-edge axis-parallel cuts (guillotine cuts) that do
not intersect any item of the solution. In this thesis, we study approximation algorithms for
the Guillotine Strip Packing problem (GSP), i.e., the Strip Packing problem where we require
additionally that the packing needs to be guillotine separable. This problem generalizes the
classical Bin Packing problem and makespan minimization on identical machines, and
thus it is already strongly NP-Hard. Moreover, it is NP-Hard to obtain a polynomial-time
\left(3/2\ -\ \epsilon\right)-approximation algorithm for GSP for any \epsilon>\ 0 (exactly as Strip Packing). We
provide a matching polynomial time \left(3/2+\epsilon\right)-approximation algorithm for GSP. Furthermore,
we present a pseudo-polynomial time \left(3/2+\epsilon\right)-approximation algorithm for GSP. This is surprising as it is NP-Hard to obtain a \left(5/4\ -\ \epsilon\right)-approximation algorithm for (general) Strip Packing in pseudo-polynomial time. Thus, our results essentially settle the approximability of GSP for both the polynomial and the pseudo-polynomial settings.
In the context of covering, we study the geometric versions of Set Cover and the related dual
Hitting Set problem, and present online and dynamic algorithms for them. In the online version
of Set Cover (resp. Hitting Set), m sets (resp. n points) are given and n points (resp. m sets) ar-
rive online, one-by-one. In the dynamic versions, points (resp. sets) can arrive as well as depart.
Our goal as before is to maintain a set cover (resp. hitting set), minimizing the size of the computed solution. For online set cover for axis-parallel squares of arbitrary sizes, we present a tight O\left(\log{n}\right)-competitive algorithm, improving upon the O\left(\log{n}\log{m}\right) general case guarantee. In the same setting for hitting set, we provide a tight O(\log\funcapply N)\ -competitive algorithm, assuming that all points have integral coordinates in \left[0,N\right)^2. No online algorithm had been known for either of these settings, not even for unit squares (apart from the known online algorithms for arbitrary set systems). For both dynamic set cover and hitting set with d dimensional hyperrectangles, we obtain \left(\log{m}\right)^{O\left(d\right)}-approximation algorithms with \left(\log{m}\right)^{O\left(d\right)} worst-case update time. This partially answers an open question posed by Chan et al. [SODA’22]. Previously, no dynamic algorithms with polylogarithmic update time were known even in the setting of squares (for either of these problems). Our main technical contributions are an extended quad-tree approach and a frequency reduction technique that reduces geometric set cover instances to instances of general set cover with bounded frequency