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Non-Self-adjoint Eigenvalue Problem for Optical Bent Waveguides
(Indian Institute of Technology Jodhpur, 2024-07-25) Hiremath, Kirankumar R.
Optics has emerged as a significant contributor to technological advancements, especially
in optical communication and optical signal processing. Nowadays, with optical waveguides, it is
possible to have all the facilities for communication and transmitting high-speed data. Due to
its importance, researchers worldwide emphasize exploring optical waveguides and their different
aspects, including design, properties, applications, and integration with other technologies.
The most prominent waveguides are straight waveguides and bent waveguides. These
waveguides are well-studied experimentally, numerically, and semi-analytically. The mathematical
aspects of the optical straight waveguides are explored very well. In this thesis, we presented
the mathematical aspects of the dielectric optical bent waveguides. The analysis was done by
constructing an eigenvalue problem governing the bent waveguide model using Maxwell’s equations
in the appropriate space setting. We restrict our-self to the 1 − D straight and bent waveguide
model. The main difficulty in studying the mathematical aspects of the bent waveguide model
was the non-self-adjointness of the bent waveguide problem. Unlike Sturm-Liouville’s theory for
self-adjoint eigenvalue problems, there is no general theory for non-self-adjoint eigenvalue problems.
It makes extracting information directly about the model associated with these problems challenging
without conducting a separate analysis.
In the Chap.1, we discussed the basics to understand how the optical waves propagate in the
planner straight and bent waveguides. The rigorous mathematical model of the straight and bent
slab waveguides with constant step-index profiles is discussed. The main objective of the model
set-up is to understand the optical wave propagation analytically in the 1−D model. The literature
survey for the optical waveguides is also a part of this chapter, where one can find the work based
on experimental, numerical, and semi-analytic studies.
For the mathematical study of the bent waveguide model, in Chap.2 we discussed some
primary results on the spectral theory of self-adjoint and non-self-adjoint operators. We conducted
a literature survey focused on the spectral theory of various non-self-adjoint operators. This survey
aimed to provide insight into methodologies for analyzing different non-self-adjoint problems.
The analytic study of the straight waveguides showed that the corresponding eigenvalues
problem is self-adjoint. It has real eigenvalues. Also, the eigenfunctions corresponding to distinct
eigenvalues are orthogonal. The analytical study of the bent waveguide was still missing due to the
non-self-adjointness of the corresponding eigenvalue problem. Our study has addressed this gap, a
part of Chap. 3. The analytic work presented in this chapter showed the non-self-adjointness of an
eigenvalue problem based on an operator theoretic setting. Here, the non-self-adjointness of the bent
waveguides problem is discussed by finding the adjoint operator of the problem. The non-self-adjoint
problem has non-real eigenvalues, which indicate the lossy nature of the bent waveguide modes. This
problem contains a bent radius parameter. The other studies show that when this parameter is large,
this problem transforms into a straight waveguide problem. In terms of the underlying mathematics,
we proved this using a transformation, showing that a non-self-adjoint problem transforms into a
self-adjoint problem. Moreover, the non-real eigenvalues of the bent waveguide problem change into
real eigenvalues of the corresponding equivalent straight waveguide problem.
An explicit relation between the real and imaginary parts of the non-real-valued propagation
constants is constructed on a detailed analysis. Based on this relation in Chap. 4, the boundedness
of both real and imaginary parts of the propagation constants is proved, meaning they are
confined within certain region in the complex plane. Furthermore, a self-adjoint problem has
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orthogonal eigenfunctions corresponding to distinct eigenvalues. For a fixed bent radius, a
1 − D semi-analytic study shows that the bent waveguide eigenvalue problem has orthogonal
eigenfunctions corresponding to distinct eigenvalues. To prove this analytically, we use the adjoint
operator and show the orthogonality behavior of the eigenfunctions. For the bent waveguides,
the asymptotic behavior of the eigenfunctions (i.e., bent modes) dictates the distribution of
electromagnetic energy in the radial directions. In this work, we showed mathematically that the
asymptotic behavior of the eigenfunctions is proportional to √1
r . This information helps to define
the appropriate function space and the subsequent mathematical analysis of the wave propagation.
Still, several mathematical questions about the bent waveguide model demand further
investigation. e.g., the stability of the model for perturbations in the system parameters, the
nature of its pseudospectra, etc. The compactness of the operator for the bent waveguide eigenvalue
problem needs to be explored to get more insights into the model. Moreover, one can extend this
work to the future 2−D set-up of the bent waveguides
Formazan-Based Metal Complexes for Applications in Resistive Switching and Electrocatalysis
(Indian institute of Technology Jodhpur, 2025-04-22) Metre, Ramesh K.
Drawing inspiration from nature, the concept of redox-active ligands explores the catalytic potential of earth-abundant metals like iron and copper despite their preference for one-electron redox reactions. Unlike traditional spectator ligands, redox-active ligands offer energetically accessible levels for reduction or oxidation, enabling oxidation state changes to occur either exclusively at the ligand or synergistically at both the ligand and metal. The incorporation of redox-active ligands presents numerous benefits, such as facilitating continuous multielectron transfer, regulating electron-deficient transition states, and enabling single-electron changes in the redox state of the metal center. In this context, we have meticulously adapted redox-active formazan-based ligands to explore a broad spectrum of applications, encompassing resistive switching memory, antibacterial properties, and electrocatalysis. Formazans boast a rich history in chemistry, where deprotonation generates monoanionic chelating N-donor ligands called "formazanates." The synthesis of formazan ligands provides a straightforward route to formazanate-based complexes with tunable electronic and steric characteristics. Complexes featuring a formazanate ligand typically exhibit a narrow HOMO–LUMO gap, resulting in energetically accessible π*-orbitals. This property renders formazanate complexes redox-active, enabling reversible storage of electrons in a ligand-based manner within these compounds. The utilization of formazanate-based ligands in coordination with base metal ions has initiated a novel research domain, expanding the range of applications in the design of magnetic, optical, and intriguing electrical materials. This is achieved by leveraging the distinctive optoelectronic properties and adaptable electrochemistry offered by formazanate ligands. The primary focus of this thesis lies in the synthesis of formazanate-based ligands, their corresponding metal complexes, and their diverse applications, ranging from resistive switching memory to antibacterial activity and electrocatalysis. An ionic organotin complex was prepared using a 2-pyridine substituted formazan ligand and investigated for its application in solid-state non-volatile write once read many (WORM) memory devices, demonstrating a high switching on-off ratio. Furthermore, distorted octahedral bis(formazanate) zinc complexes were used in the fabrication of a memory device that intriguingly exhibited non-volatile resistive switching memory behavior. The bis(formazanate) iron complexes displayed extensive redox behavior during the cathodic sweep in cyclic voltammetry analysis and were realized as electroactive cathode materials for the electrocatalytic H2O2 reduction in one-compartment H2O2 fuel cell. Later, a mono(formazanate) mercury complex was prepared and was further studied as an antimicrobial agent.
Computer-aided Diagnostic System for Hypertensive and Diabetic Retinopathy
(Indian Institute of Technology Jodhpur, 2025-04-21) Tiwari, Anil Kumar
Retinal diseases such as Diabetic Retinopathy (DR) and Hypertensive Retinopathy (HR) are serious health concerns. HR is a retinal disease caused by elevated blood pressure for a prolonged period. Diabetic Retinopathy(DR)is a progressive retinal disease caused by long-term diabetes.
Non-proliferative diabetic retinopathy(NPDR) is an early stage of DR, damages blood vessels of the retina. Moreover, HR serves as a biomarker for several illnesses, including retinal diseases, atherosclerosis, strokes, kidney disease, and cardiovascular risks. Early identification of these diseases helps in the timely and proper treatment can prevent blindness. Manual diagnosis of
these retinal diseases is time-consuming, resource demanding, inconvenient, costly, and demands
specialized skills and experience. On the other hand, Computer-aided diagnosis (CAD) and
Artificial intelligence (AI) based systems are expected to solve the above-mentioned challenges
effectively. This thesis proposes an efficient algorithm for HR detection. Further, for effective management of these diseases, we develop an effective algorithm for severity grading of HR and NPDR. To achieve this, a careful study of existing literature in the field of automatic diagnosis of
HR and DR is conducted to identify important research gaps in this area. It has been observed that the availability of public data sets for HR diagnosis is limited. Moreover, there is no such public dataset available for HR grading. Severity grading helps in the timely and effective management of
these diseases and reduces future risks. However, very limited research has been conducted for the severity grading of HR and NPDR. Additionally, previous studies mainly relied on Arteriovenous
Ratio (AVR) and the manual selection of regions of interest (ROI) around the optic disc (OD) for
HR detection and its grading.
Due to ROI selection primarily around OD, these method had risk of missing several
important clinical features present elsewhere, resulting in less accurate diagnostic outcomes.
Furthermore, one of the key challenges observed in DR and HR severity grading is the high-class
imbalance high-class imbalance. Such class imbalance makes the training of learning based recognition models very challenging, as the majority of class samples predominate in the training process of the learning model.
To address these limitations, a novel HR detection approach has been proposed, based on few-shot learning, using a pretrained initial baseline model to obtain transferable knowledge for
feature embedding on few-shot prediction. This approach aims to reduce overfitting and improve
generalization, which is especially advantageous for smaller datasets. Unlike previous methods,
the proposed approach uses complete images to capture all clinical features. Experimental results
demonstrate the effectiveness of the proposed HR detection method.
In this thesis work, we develop “HRSG: Expert-Annotated Hypertensive Retinopathy
Severity Grading Dataset” dataset, encompassing fundus images, and categorizing the severity
into four classes: normal, mild, moderate, and severe. The grading process is conducted by three
experienced ophthalmologists affiliated with prestigious medical institutions in India, including the
All India Institute of Medical Sciences (AIIMS) in Jodhpur, the Aravind Eye Hospital in Madurai,
and the Sri Aurobindo Institute of Medical Sciences Hospital in Indore.
For effective severity grading of HR, a hybrid deep learning (DL) architecture is proposed
that leverages the combined strengths of pretrained ResNet-50 and a modified Vision Transformer
(ViT) enhanced with both global and locality self-attention mechanisms, enabling accurate grading
v
into four classes: normal, mild, moderate, and severe. The proposed method effectively captures
both local and global contextual information across the input image, leading to a robust and
resilient classification model. Further, to address the class imbalance issue, we introduce a
novel decouple representation and classifier (DRC) based training method. The proposed DRC
method effectively addresses the class imbalance by improving the module’s capacity to identify
effective feature learning while maintaining the original dataset’s distributional properties, leading
to improved diagnostic accuracy. The extensive experimental results demonstrate the effectiveness
of the proposed method in accurately grading HR severity.
This thesis also presents a reliable method for NPDR severity grading into normal, mild,
moderate, and severe classes. This method includes an initial image enhancement to improve quality
for subsequent processing. A feature set is then developed using various descriptors, capturing
rich information to identify distinct and unique properties of NPDR lesions. To address the
class imbalance, we employ the Synthetic Minority Oversampling Technique (SMOTE) and an
ensemble-learning-based Random Forest (RF) classifier to improve the model’s performance on the
imbalance classes. Moreover, the comparison results show that the proposed method performs
better than existing methods, making it suitable for the early diagnosis and effective management
of NPDR.
The contributions of this thesis aim to assist healthcare professionals in early HR detection,
regular screening, risk stratification, and patient categorization based on HR and NPDR severity
grading. These developments aim to optimize clinical decision-making, improve resource allocation,
and enhance overall disease management. The proposed systems can assist clinicians in referral
decisions and facilitate mass screening.
Computer-aided Dignostic System for Hypertensive and Diabetic Retinopathy
(Indian Institute of Technology Jodhpur, 2025-04-21) Tiwari, Anil Kumar
Retinal diseases such as Diabetic Retinopathy (DR) and Hypertensive Retinopathy (HR) are
serious health concerns. HR is a retinal disease caused by elevated blood pressure for a prolonged
period. Diabetic Retinopathy(DR)is a progressive retinal disease caused by long-term diabetes.
Non-proliferative diabetic retinopathy(NPDR) is an early stage of DR, damages blood vessels of
the retina. Moreover, HR serves as a biomarker for several illnesses, including retinal diseases,
atherosclerosis, strokes, kidney disease, and cardiovascular risks. Early identification of these
diseases helps in the timely and proper treatment can prevent blindness. Manual diagnosis of
these retinal diseases is time-consuming, resource demanding, inconvenient, costly, and demands
specialized skills and experience. On the other hand, Computer-aided diagnosis (CAD) and
Artificial intelligence (AI) based systems are expected to solve the above-mentioned challenges
effectively. This thesis proposes an efficient algorithm for HR detection. Further, for effective
management of these diseases, we develop an effective algorithm for severity grading of HR and
NPDR.
To achieve this, a careful study of existing literature in the field of automatic diagnosis of
HR and DR is conducted to identify important research gaps in this area. It has been observed that
the availability of public data sets for HR diagnosis is limited. Moreover, there is no such public
dataset available for HR grading. Severity grading helps in the timely and effective management of
these diseases and reduces future risks. However, very limited research has been conducted for the
severity grading of HR and NPDR. Additionally, previous studies mainly relied on Arteriovenous
Ratio (AVR) and the manual selection of regions of interest (ROI) around the optic disc (OD) for
HR detection and its grading.
Due to ROI selection primarily around OD, these method had risk of missing several
important clinical features present elsewhere, resulting in less accurate diagnostic outcomes.
Furthermore, one of the key challenges observed in DR and HR severity grading is the high-class
imbalance high-class imbalance. Such class imbalance makes the training of learning based
recognition models very challenging, as the majority of class samples predominate in the training
process of the learning model.
To address these limitations, a novel HR detection approach has been proposed, based on
few-shot learning, using a pretrained initial baseline model to obtain transferable knowledge for
feature embedding on few-shot prediction. This approach aims to reduce overfitting and improve
generalization, which is especially advantageous for smaller datasets. Unlike previous methods,
the proposed approach uses complete images to capture all clinical features. Experimental results
demonstrate the effectiveness of the proposed HR detection method.
In this thesis work, we develop “HRSG: Expert-Annotated Hypertensive Retinopathy
Severity Grading Dataset” dataset, encompassing fundus images, and categorizing the severity
into four classes: normal, mild, moderate, and severe. The grading process is conducted by three
experienced ophthalmologists affiliated with prestigious medical institutions in India, including the
All India Institute of Medical Sciences (AIIMS) in Jodhpur, the Aravind Eye Hospital in Madurai,
and the Sri Aurobindo Institute of Medical Sciences Hospital in Indore.
For effective severity grading of HR, a hybrid deep learning (DL) architecture is proposed
that leverages the combined strengths of pretrained ResNet-50 and a modified Vision Transformer
(ViT) enhanced with both global and locality self-attention mechanisms, enabling accurate grading
v
into four classes: normal, mild, moderate, and severe. The proposed method effectively captures
both local and global contextual information across the input image, leading to a robust and
resilient classification model. Further, to address the class imbalance issue, we introduce a
novel decouple representation and classifier (DRC) based training method. The proposed DRC
method effectively addresses the class imbalance by improving the module’s capacity to identify
effective feature learning while maintaining the original dataset’s distributional properties, leading
to improved diagnostic accuracy. The extensive experimental results demonstrate the effectiveness
of the proposed method in accurately grading HR severity.
This thesis also presents a reliable method for NPDR severity grading into normal, mild,
moderate, and severe classes. This method includes an initial image enhancement to improve quality
for subsequent processing. A feature set is then developed using various descriptors, capturing
rich information to identify distinct and unique properties of NPDR lesions. To address the
class imbalance, we employ the Synthetic Minority Oversampling Technique (SMOTE) and an
ensemble-learning-based Random Forest (RF) classifier to improve the model’s performance on the
imbalance classes. Moreover, the comparison results show that the proposed method performs
better than existing methods, making it suitable for the early diagnosis and effective management
of NPDR.
The contributions of this thesis aim to assist healthcare professionals in early HR detection,
regular screening, risk stratification, and patient categorization based on HR and NPDR severity
grading. These developments aim to optimize clinical decision-making, improve resource allocation,
and enhance overall disease management. The proposed systems can assist clinicians in referral
decisions and facilitate mass screening.
vi
Heat Transfer Analysis on the Expedition of Temperature Distribution and Bubble Behavior from Nucleation to Critical Heat Flux during Pool Boiling
(Indian Institute of Tehcnology, Jodhpur, 03-07-2023) Kothadia, Hardik B.
The phase change heat transfer processes are widely implemented for heat extraction as they utilise both sensible and latent heat (Rohsenow and Griffith, 1955). The capability to remove the higher magnitude of heat at low wall superheats, and the lack of moving parts makes pool boiling appealing (Memmott and Manera, 2011). Pool boiling is economical, simple, and prevalent among all available cooling schemes. The utilization of the aforementioned technique is widely implemented for thermal management in nuclear industries and in microelectronic devices. Conventional air cooling systems cannot handle these devices cooling requirements which may be due to their low heat transfer performance. In such instances, pool boiling, and droplet evaporation techniques can be implemented. Nowadays, the nuclear industries, renewable energy sectors, and power plants are implementing compact heat exchangers as preheaters, regenerators, and intermediate heat exchangers (Pattanayak et al., 2022) (Pattanayak and Kothadia, 2020). These compact heat exchangers are basically of tubular or plate-type. Therefore it gives the urge to study the heat transfer characteristics of those heat exchangers and analyse the methodologies that can enhance the heat transfer from the surface of tubes and plates (Pattanayak et al., 2022).
The lack of qualitative theories, quantitative data, and explanations in the area of critical heat flux (CHF) in tube and plate makes it an interesting domain of research. There is limited research explaining the effect of high, substrate and liquid temperatures, on droplet evaporation. There is a scarcity of research in analysing the heat transfer coefficient during the evaporation process (Pattanayak et al., 2021) (Pattanayak and Kothadia, 2022). The research highlights the critical heat flux (CHF) studies on mini-channels, micro-channels, and plates during pool boiling under uniform heat flux conditions. Identification of the tube and plate length and diameter beyond which CHF becomes independent of the dimensions is discussed. The effect of tube and plate orientations and pool subcooling on CHF has been analysed. Different regimes of pool boing under uniform heat flux conditions are discussed based on bubble behavior. The instantaneous heat transfer coefficient during droplet evaporation is analysed. The CHF data are used to derive an empirical correlation that includes the impact of subcooling, orientation, and dimensions (Pattanayak et al., 2023). In the case of the analysis of compact heat exchangers, SS 304 tubes and plates are used. The orientation is changed from 0ᵒ to 90ᵒ for tubes and 0ᵒ to 180ᵒ for plates. The length and diameter of tube is varied from 50 mm to 1000 mm and 1.2 mm to 9 mm, respectively. The water pool is kept at 30°C, 50°C, 75°C, and saturation temperature. The length of the plate is varied from 50 mm to 300 mm. The width of the plate ranges from 10 mm to 20 mm. The pool is maintained at 25℃ and saturation temperature corresponding to ambient pressure. It has been noted that the severity of CHF lessens as pool temperature rises. For a particular pool temperature, the shortest length has a higher magnitude of CHF. As tube diameter and width expand, CHF values decrease. In the case of tubes, the CHF value is larger for horizontal orientation than vertical orientation.In the case of the analysis of compact heat exchangers, SS 304 tubes and plates are used. The orientation is changed from 0ᵒ to 90ᵒ for tubes and 0ᵒ to 180ᵒ for plates. The length and diameter of tube is varied from 50 mm to 1000 mm and 1.2 mm to 9 mm, respectively. The water pool is kept at 30°C, 50°C, 75°C, and saturation temperature. The length of the plate is varied from 50 mm to 300 mm. The width of the plate ranges from 10 mm to 20 mm. The pool is maintained at 25℃ and saturation temperature corresponding to ambient pressure. It has been noted that the severity of CHF lessens as pool temperature rises. For a particular pool temperature, the shortest length has a higher magnitude of CHF. As tube diameter and width expand, CHF values decrease. In the case of tubes, the CHF value is larger for horizontal orientation than vertical orientation.In the case of the analysis of compact heat exchangers, SS 304 tubes and plates are used. The orientation is changed from 0ᵒ to 90ᵒ for tubes and 0ᵒ to 180ᵒ for plates. The length and diameter of tube is varied from 50 mm to 1000 mm and 1.2 mm to 9 mm, respectively. The water pool is kept at 30°C, 50°C, 75°C, and saturation temperature. The length of the plate is varied from 50 mm to 300 mm. The width of the plate ranges from 10 mm to 20 mm. The pool is maintained at 25℃ and saturation temperature corresponding to ambient pressure. It has been noted that the severity of CHF lessens as pool temperature rises. For a particular pool temperature, the shortest length has a higher magnitude of CHF. As tube diameter and width expand, CHF values decrease. In the case of tubes, the CHF value is larger for horizontal orientation than vertical orientation.The study demonstrates that for horizontally oriented tubes, CHF fluctuation is negligible beyond a length of 500mm, regardless of diameter. According to the study performed for vertical channels, CHF fluctuation is negligible for tubes with a diameter more than 2.5 mm beyond a length of 200 mm. The vertical orientation of the plates results in a higher CHF magnitude as compared to the horizontal upward and downward orientations respectively (Pattanayak and Kothadia, 2020), (Pattanayak et al., 2021), (Pattanayak et al., 2023). The hydrophobic surface of copper electrodeposited tubes exhibits a lesser CHF magnitude than the uncoated surface and is efficient for phase change heat transfer applications in lower heat flux regimes. Furthermore, the analysis of heat transfer during droplet evaporation is conducted to study the effect of surface and liquid temperature on the instantaneous heat transfer coefficient. It is observed that the evaporation rate is higher for copper than aluminum. The instantaneous heat transfer coefficient increases with the temperature of droplet evaporating on a given substrate and is higher for copper. When substrate temperature increases for a given droplet temperature, the instantaneous heat transfer coefficient increases (Pattanayak and Kothadia, 2021) (Pattanayak et al., 2022). The regimes from natural convection to CHF limit in a subcooled pool of water maintained under uniform heat flux conditions are studied for SS 304 upward-facing plates of different dimensions (Clifton and Chapman, 1969) (Pattanayak et al., 2022). During the heat transfer process, the temperature distribution along the plate is examined. The Nusselt number is seen to be independent of aspect ratio (Pattanayak et al., 2022) (Pattanayak and Kothadia, 2022). The Nusselt number rises when the plate length and width are independently increased. The study is also carried out in saline water of solutions with varying salinity from 0%, 0.2%, 0.5%, and 2%, and is observed that beyond salinity 0.2%, the heat transfer coefficient decreases (Pattanayak et al., 2022).