Indian Institute of Science Bangalore
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Ultrawideband and wide-angle scan antenna element and small active phased arrays
No full textWideband, wide-scan active phased arrays (APA) are widely used for multi-function radars, communication and electronic warfare. Although considerable research is available on the design and analysis of such antenna elements and arrays with large aperture, multi-octave wide scan phased antenna arrays with an electronically small aperture finds major application in electronic warfare (EW), is not well-developed. Based on a detailed literature survey on ultrawideband antenna for the wideband APA this research began with investigating different designs of tapered slot antenna (TSA) elements.
A study of the performance parameters like bandwidth, beamwidth, cross-polarization and beam-squint have been conducted for candidate antenna elements such as microstrip fed TSA, balanced antipodal TSA and stripline fed TSA (STSA). Based on these studies, STSA was selected as the most suitable candidate for meeting the requirement for antenna element. An STSA element with a wide beamwidth of 120° in H-plane with reflection coefficient less than -10 dB is designed.
Two different antenna arrays are proposed in this research to demonstrate the advantages of STAS as small aperture active array element for wideband phased arrays. Challenges in the design, analysis and characterization of moderately sized phased arrays using STSA element have been analyzed. Although seof interest in literature, of these a linear active phased array antenna that operates across 6 to 18 GHz frequency range, an array with wide-scan coverage of ±60° in H-plane is not developed.
The element pattern in phased arrays causes a squint in the main beam away from broadside. For small phased arrays this can be reduced by on-line calibration by taking a sample of signal at each element of the array. Therefore STSA is integrated with a -20 dB asymmetrical coupler at the feed for calibration and performance monitoring. In addition, the proposed STSA with integrated coupler is designed to have a wideband transition which allows a direct 50 Ω stripline feed. The isolated port of the coupler is internally terminated with a resistor using Ohmegaply resistive layer to improve reliability in airborne platform.
A linear array of 16 elements is designed and experimentally demonstrated. The main figure of merit of the array is realised gain of the array over the scan angle. A minimum element gain of 0 dB in array environment is obtained over the scan angle of ±60°, without any grating lobes at high frequency. It also demonstrated a cross-polarization of better than -25 dB at boresight and beam squint less than 1°. A staggered feeding arrangement is incorporated to accommodate the physical dimensions of connectors for minimum inter element spacing.
Conventionally the centre element pattern in array environment is used for obtaining the scanning characteristics of a large phased array. But, for small phased array, since the edge effects may be significant an average scan element pattern is proposed for array characterization. This gives an accurate result for the scan characteristics of array and can be used to correct array synthesis before full scale fabrication. This approach is validated by measuring the array pattern of the fabricated array with transmit/receive module.
Second, an 8 element E-plane array operating over 1 to 6 GHz frequency range is proposed with scanning of 45° from broadside. This antenna covers D, E, F and G bands of EW system. A novel STSA has been investigated across this bandwidth. Here the radiating part of tapered slot antenna is ended with an elliptical stub instead of circular stub which gives the same performance that of circular stub with reduced overlap with the radial stripline stub.
A compact broadband Wilkinson power divider feed network is designed along with array to characterise this. These edge effects are more severe in this array, especially at the low frequency of the operation band and methods to overcome this are investigated. Approaches of additional dummy edge elements or modifying edge elements have been investigated by simulations to reduce edge effects. An approach of adding 3D caps at the edges has been found to be more effective in this regard.
To summarize, methods for designing high performance multi-octave stripline fed tapered slot antenna elements and their arrays in the E- and H-plane have been developed using simulations and validated by experiments. These antennas are particularly suited as small aperture arrays in EW applications
Collective Phototaxis of Chlamydomonas reinhardtii Cells
No full textMicroorganisms are omnipresent in our life and the environment, such as microbes in the gut, spermatozoa in reproductive organs, algae and protozoa in the aquatic ecosystem, and bacterial colonization and infection. Motility in microorganisms is an essential feature of life that facilitates the search for food, avoidance of possible life-threatening cues, and spatially distributing cells for thriving. Often taxis phenomena wherein microorganisms exhibit directed motion in response to external physio-chemical stimuli or nutrient gradients constitute a coordinated complex movement of a large collection of microorganisms such as phototaxis of phytoplankton in response to light and chemotaxis of bacteria or sperm cells in response to a chemical gradient. Therefore, it is essential to understand the effect and origin of emerging collective behavior in dense suspension and the nature of crossover from an individual cell to the population level.
This thesis presents a comprehensive experimental study of collective behavior in phototaxis of Chlamydomonas reinhardtii (CR) cells, a single-cell biflagellate microswimmer widely considered as model organism. We divide the study of phototaxis into three major parts - (i) steady-state phototactic response of cells (when cells are already oriented towards the light exhibiting directed motion), (ii) Response: transition from random motion of cells to steady-state directed phototactic motion when light is switched on (iii) Recovery: transition from steady-state directed phototactic motion of cells to random motion when light is switched off.
In the first part of the thesis, we describe the steady-state phototactic response of CR cells. We show that at a given light intensity, the phototactic efficiency of CR cells is minimal (even lower than a single isolated cell) at a well-defined threshold cell concentration, above which the efficiency of a large collection of cells can even exceed the efficiency obtainable from a single isolated cell. We demonstrate that the origin of enhancement in phototactic efficiency in collective regime lies in the slowing down cell speed, leading them to better light sensing capabilities. We further show that the steady-state phenomenology observed in this study is well captured by modeling the phototactic response as an active Brownian particle subject to density-dependent external aligning torque.
In the second part, we discuss the kinetics of phototactic reorientation during - (i) Response and (ii) Recovery. Due to the single eyespot in unicellular microorganisms, navigation to the light source in a three-dimensional world entails a specific control mechanism. The mechanism consists of detecting light direction by comparing light intensity while moving on a helical path and then translating that information to motility apparatus such as flagella which consequently turns the microorganism towards the light source. We show that the response kinetics, i.e., dynamics of photo turn of a population of CR cells, depends on the cell concentration and light intensity. The response time is faster and independent of stimulus light intensity at low cell concentrations. In contrast, at high cell concentrations, the response is slower and depends non-monotonically on the light intensity. We show that such effects on the response kinetics originate from the coupling between swim speed and received photon flux.
Further, in the second part, we present the results on the recovery (orientational diffusion) of cells that have already achieved a steady state phototactic motion. The kinetics of orientational recovery of oriented cell population reveals a characteristic time independent of their cell concentration and light intensity. Finally, we extend our model of active Brownian particle subject to aligning torque to capture the time-dependent reorientation process.
These results demonstrate that cell populations modulate fundamental quantities such as phototactic efficiency and response time. Coupling between collective effects and external physio-chemical stimuli results in complex modulation of single-cell behavior in the dense suspension. We have elucidated a simple physical and phenomenological mechanism governing such complex collective behavior.Wellcome Trust/DBT India Alliance Fellowshi
Interfacial Studies Using Organized Organic and Inorganic Films
No full textInterfaces play an important role in various fields, such as catalysis, charge transfer / electrochemical processes, chemical reactions, molecular electronics, wetting, and biology. Building functional structures with a perfect, uniform, and organized arrangement is one of the foremost requirements in understanding interfacial properties, particularly for molecular electronics, sensors, and other niche applications based on advanced materials. In addition, fundamental aspects of properties and reactions of molecules / materials confined within a limited-size space enhance the understanding of the effects of proximity. Assembling molecules at water-air interfaces in a Langmuir trough offers exquisite control over the molecular organization, packing, and orientation. The dynamic nature of applied surface pressure (ranges to a few dozen megapascals) is an additional merit of the Langmuir monolayer, which affects the orientation and the relative intermolecular distance (proximity between the molecules).
In the present study, the effect of surface pressure on the organized assembly of anilinium ions at the air-water interface during the in-situ electro-polymerization in a Langmuir trough is studied. The applied surface pressure on the monolayer (EGO-anilinium complex) during the in-situ electro-polymerization leads to the preferential formation of the polaronic form of polyaniline. The absence of applied surface pressure on the monolayer during the electro-polymerization results in the twisted bipolaronic form. Different PANI forms are subsequently subjected to understanding their characteristics toward electrochemical actuation, hygro-actuation, and electrochemical hydrogen evolution reaction. In the second aspect of organic assembly, the proximity effect in a Langmuir monolayer is used to investigate the possibility of abiotic formation of an amide from an acid and an amine. As for inorganic systems, 2D chalcogenides (MoSSe, VPS3) are assembled at the air-water interface, and the aligned monolayers of molybdenum chalcogenides are used for surface-enhanced Raman scattering studies. In a separate section, the lithium-ion charge storage characteristics of a conjugated Schiff-base polymer based on a diazabutadiene unit are studied
Understanding the mechanisms of polarity establishment and nuclear envelope breakdown in Caenorhabditis elegans embryos
No full textPolarity establishment is critical for the development and stem cell lineages. The one-cell stage of the Caenorhabditis elegans embryo polarizes soon after fertilization. As a result, the first division of the embryo is asymmetric. The parent P0 cell divides into a large AB and a smaller P1 cell. The AB daughter cell specifies the somatic lineage, while the P1 cell lineage forms the germline. Failure to accurately establish polarity results in embryonic lethality. It is well-established that centrosomes are responsible for determining the axis of polarity in the one-cell embryo; however, the identity of the centrosome-associated polarity cue and the precise mechanism of polarity establishment remained unknown.
After polarity establishment, the one-cell C. elegans embryo enters in mitotic phase, where the male and female pronuclei expand their size and condense their chromatin. The two pronuclei migrate towards each other, followed by the nuclear envelope breakdown (NEBD) that allows the mixing of the maternal and paternal genomes. Subsequently, the mitotic spindle is assembled, and parental genomes are aligned on the metaphase plate. At the onset of anaphase, the differential cortical pulling forces position the mitotic spindle towards the embryo posterior. Since the position of the mitotic spindle dictates the site for cleavage furrow/cytokinesis, this leads to unequal cell division, producing a larger anterior AB cell and posterior smaller P1 cell. The process of NEBD is conserved in all metazoans that undergo 'open' mitosis and is vital for the accurate segregation of the chromosomes. However, the precise mechanism by which this occurs is poorly understood.
In the first part of my thesis, I have characterized the role of conserved mitotic kinase Aurora A in proper polarity establishment in the one-cell C. elegans embryo. In the second part of this work, for the first time, we link the function of phosphatase with the NEBD. We show that the PP2A-B55/SUR-6 (hereafter referred to as B55/SUR-6) is essential for proper NEBD in C. elegans embryos.
(1) Aurora A kinase/AIR-1 gradient at the centrosomes ensures singularity in the polarity axis in the one-cell C. elegans embryo
Proper cell polarization is vital for generating functional asymmetry within cells, which is crucial for development. In one-cell C. elegans embryo, centrosomes are responsible for polarity establishment, i.e., anterior-posterior body axis formation. Centrosomes are hypothesized to form a protein gradient that diffuses out to the cortex and disassembles the actomyosin network, thereby breaking symmetry and concomitantly establishing distinct domains of anterior and posterior conserved polarity proteins, PAR proteins. Primary candidate/s and the precise mechanism by which the centrosome achieves symmetry breaking remained elusive. We uncovered that RNAi-mediated depletion of conserved mitotic kinase, Aurora A kinase (AIR-1 in C. elegans) in the one-cell embryo disrupts stereotypical actomyosin-based cortical flows that occur at the time of polarity establishment. This misregulation of actomyosin dynamics leads to the formation of two posterior polarity axes. Also, we found that this function of Aurora A in polarity establi= shment is dependent on its kinase activity. Notably, this impact of Aurora A depletion is independent of its central role in microtubule nucleation. Interestingly, centrosome positioning in dictating the posterior polarity axis (or PAR-2 localization) is no longer important when Aurora A is depleted in the one-cell embryo. The mechanism by which Aurora A directs symmetry breaking is likely through direct regulation of RhoA-dependent contractility since we observed rescue in the formation of a single polarity axis in Aurora A (RNAi) embryos that are co-depleted of Rho-GEF, ECT-2. Further, a previous study showed that ECT-2 de-localizes from the posterior cortex at the time of polarity establishment, presumably under the influence of centrosome-mediated polarity cue. Our study shows that in the absence of Aurora A, ECT-2 fails to de-localize from the posterior cortex at polarity establishment, providing a possible explanation for the impaired actomyosin flow seen in Aurora A (RNAi) embryos. In summary, our work has contributed to uncovering an unconventional role of Aurora A kinase in polarity establishment in C. elegans. Thus, we propose that Aurora A gradient at the centrosome is a key for symmetry breaking and thus for ensuring proper polarity set-up.
(2) B55/SUR-6 promotes nuclear envelope breakdown in the C. elegans one-cell embryo
The nucleus constrains the cell's genetic material by forming a selective barrier to the entry of macromolecules from the cytoplasm. In animal cells, NEBD enables the spindle microtubules to access and attach to the chromosomes within the nucleus during mitosis. Proper chromosome-microtubule attachment ensures faithful segregation of genetic material into the two daughter cells. NEBD is regulated by the activity of critical kinases such as CDK-1, AIR-1 (Aurora A), and PLK-1. While these mitotic kinases are crucial for NEBD, no phosphatase has yet been linked with NEBD at the mitotic entry. Here, we identified B55/SUR-6 as an essential regulatory subunit of PP2A phosphatase critical for timely NEBD in the one-cell C. elegans embryo. We found that in embryos that are depleted for B55/SUR-6, nuclear membrane permeabilization (NEP) is significantly delayed, and nuclear lamin and nucleoporins persist throughout mitosis. As a result, chromosomes' segregation is impaired. Notably, we found that the impact of B55/SUR-6 depletion on NEBD is not because of its effect on cell cycle progression or mislocalization of essential kinases such as PlK-1 or AIR-1. We uncovered that B55/SUR-6 acts redundantly with microtubule-generated pulling forces to promote NEBD efficiently. Further, genetic epistasis experiments suggest that nuclear lamin (LMN-1), but not nucleoporin/s, is the target of B55/SUR-6. Notably, genomically-tagged GFP-B55/SUR-6 localizes to the nucleus before the onset of NEBD, suggesting that B55/SUR-6 nuclear import may directly promote NEBD. Overall, these findings link the PP2A phosphatase complex to a critical process of NEBD in animal cells.
In summary, my work has contributed to the mechanistic aspects of the two processes: polarity set-up and nuclear envelope breakdown, which are vital for the establishment and the continuity of life
Robust Numerical Modeling of Adhesively-Bonded Joints for Safety Assessment of Vehicle Body Structures Subjected to Extreme Loading
No full textContinuous adhesively-bonded joints can lead to stiffer vehicle body structures in contrast to conventional spot-welded steel sheet metal-based unitized vehicle body design. For a given target stiffness, adhesive bonding, in lieu of spot welding, can thus provide scope for lightweighting which in turn can make vehicles more fuel efficient. The performance of adhesively bonded joints, however, has not been adequately proven under severe dynamic loading conditions such as arising from impact and blast-induced shock wave propagation. There is also a deficiency in published literature on robust numerical modelling of adhesively-bonded joints exhibiting predominantly shear and peel stresses, and applying the same towards prediction of the behavior of structural components such as steel hat sections subjected to axial and transverse impact. Additionally, the system-level performance of adhesively-bonded joints in full vehicle body design under extreme loading conditions, which probably goes beyond the general purview of academic research, does not appear to have been reported in open literature.
Keeping the above points in mind, the current research is aimed at systematically studying the mechanical behaviors of adhesively-bonded joints with steel substrates at coupon, component and full vehicle levels with a judicious combination of physical testing and nonlinear explicit finite element analysis (FEA). With the stated objective, coupon specimens of various joint configurations have been tested in a UTM to begin with till failure, and their behaviors reproduced using cohesive zone modeling in LS-DYNA, an explicit contact-impact FEA solver, with uncoupled mode I and mode II fracture mechanics properties. The right constitutive model had to be arrived at through extensive comparison of relevant material models including those based on von Mises and Drucker-Prager yield criteria for classical elasto-plastic stress-strain behaviors of materials. As part of the systematic study envisioned, thin-walled hollow members with double-hat sectional profiles of a given length were fabricated with spot welding, only adhesive bonding, and with hybrid joining i.e. predominantly adhesive bonding with sparse spot welding. These specimens were then subjected to axial and transverse impact loading in a drop-weight test setup. Not only valuable insights into the relative behaviors of the components of diverse joining techniques were obtained, but also the nonlinear dynamic responses of the components became valuable data for further validating the finite element (FE) modelling procedure developed previously at the level of coupon specimens. With an emphasis on real-world applications, conventional spot welded front rails were replaced in turn with only adhesively-bonded and hybrid welded-bonded rails, in a detailed FE model of a compact passenger car and subjected to full frontal impact against a rigid barrier as in a US-NCAP test with a closing speed of 56 kmph. This study provided a framework for assessing the performance of a purely adhesively-bonded rail in a full vehicle crash test. Finally, using an ALE (Arbitrary Lagrangian-Eulerian) modelling procedure, the effect of an underbody blast under a vehicle resulting in a shock wave propagating through the ambient air and striking underneath the floor of a vehicle was captured and the potentially severe injury caused to the lower limb of an occupant predicted. In this connection, the FE model of a military lower leg extremity (MIL-LX) anthropomorphic test device was formulated and various novel floor-based countermeasures with spot welding and adhesive bonding compared for mitigation of lower limb injuries to vehicle occupants
Rice transcription factors OsMADS2 and OsMADS4 regulate floret organ development: Deciphering their gene targets, traits and functions related to their unequal genetic redundancy
No full textOrgans in modern dicot flowers are positioned in concentric rings (whorls). The outermost whorl has green protective sepals, internal to which are showy petals, and the reproductive stamen and carpel whorls. Florets of rice, cereals and grasses evolved certain morphological and functionally distinct features in their non-reproductive organs. Striking among them are the highly modified petal analogs; called lodicules, and the large bract-like outermost organs named palea and lemma. The analogy of these modified rice floret organs to sepals and petals is debated. The two lodicules of rice florets are small (limited growth in Proximal-Distal axis), thick (extensive growth in Dorsal-Ventral axis) and are asymmetrically positioned to occupy only one half of the second whorl. They perform an important mechanical role in the partial opening of the flower for stamen emergence and subsequent closing. Their asymmetric position, small fleshy structure with many parenchymatous cell layers and their regulated physiology for swelling and collapse are critical for these functions. Understanding the developmental mechanisms of these organs that underlie their function is of direct interest to evo-devo plant biologists and breeding programs aimed at crop yield improvement. Given these implications, for a deeper understanding of plant development and potential future uses in crop breeding, we define the objectives of this study and report our key findings
Objective 1: Uncovering the gene targets of rice class B PISTILLATA-like (PI-like) factors that regulate lodicule and stamen development
Objective 2: Characterizing an OsMADS2 target gene; AP2/EREBP86 encoding AINTEGUMENTA-like/PLETHORA (AIL/PLT) family transcription factor.
Overall, this study expands our knowledge on traits and molecular mechanisms controlled by rice class B PI-like factors: OsMADS2 and OsMADS4, and provides new insights on their functional divergence that greatly extend our understanding of lodicule and stamen development. This study sheds light on some molecular mechanisms triggered by
AP2/EREBP86 that can initiate and maintain shoot meristem fate which have the potential to improve somatic embryogenesis
Active matter: chirality, translational order, and interfaces
No full textMy PhD work is on chiral active matter with solid and fluid directions, dynamics of the
interface of a nonconserved chiral order parameter in an active system, flocking on curved
manifolds and field-driven colloids in confined nematics.
We start by formulating theories of layered active chiral matter. We
start with constructing the active model H* in two and three dimensions – the chiral
and active variant of model H. This theory describes the coupled dynamics of a conserved
scalar order parameter and a conserved momentum density field.
At thermal equilibrium, chiral molecules form a range of liquid-crystalline phases such
as cholesteric, with a helical structure of the molecular orientation. It turns that at long length scales, the mechanics of a cholesteric is precisely the same as that of a smectic
A which has an achiral one-dimensional density modulation. It is curious that
though microscopic chirality leads to a one-dimensional periodic structure, its asymptotic
long-wavelength elasticity and hydrodynamics show no signature of chirality. In this
chapter we show that this equivalence does not carry over to active cholesteric and
smectic A phases. Thanks to the presence of a mix of solid- and liquid-like
directions, we predict that chiral active stresses create a force density tangent to contours of constant mean curvature of the layers. This non-dissipative force in a fluid direction
– odder than odd elasticity – leads, in the presence of an undulational instability
created by non-chiral active stresses normal to the layers, to spontaneous vortical flows
arranged in a two-dimensional array with vorticity aligned along the pitch axis and
alternating in sign in the plane. This vortex-lattice state can be switched on or off by
means of an externally imposed uniaxial stress. We also show that a two-dimensional
active cholesteric is unstable with an activity threshold that goes to zero for an infinite
system.
We then move on to formulating the active hydrodynamics of columnar phases,
those with two solid and one fluid direction. We show that a bulk active columnar
phase is spontaneously unstable to an extensile activity along the column direction via a
buckling instability. We predict singular stiffening or softening – depending on whether
the active achiral stress is contractile or extensile – of the buckling of fluid columns in all
active columnar materials, irrespective of whether they are chiral or polar. Further, we
demonstrate that the effect of the active achiral stress in columnars is exactly equivalent
to an externally imposed in-plane, isotropic stress; therefore, the instability induced by
a singular softening of the column buckling mode – in extensile systems – is exactly
equivalent to a columnar Helfrich-Hurault instability under an external stress. This
allows us to exactly calculate the threshold activity for this instability in a finite columnar
liquid crystal. The instability is mediated by a twist-bend mode resulting in helical
columns – same as those that arise from a Helfrich-Hurault instability of passive columnar
material. If the active units composing the columnar state are in addition chiral, the
buckled and twisted state beyond the spontaneous Helfrich-Hurault instability in an
apolar system hosts large-scale shear flows due to a new form of odd elasticity. For
polar and chiral columnar systems, we show that two-dimensional solid odd elasticity is
naturally realised in this three-dimensional material. The interplay of this odd elasticity
with viscous, Stokesian hydrodynamics leads to an optical mode with a frequency that depends on the direction of the relative angle between the wavevector direction and
polarity but, crucially, not on the wavenumber. The frequency of this vibrational mode
is set by the ratio of the coefficient of chiral and polar active stress and the viscosity.
The damping of this mode is also wavenumber-independent. The oscillation is due to
the two in-plane displacement fields acting effectively as a position-momentum pair.
In chapter 4, we move to investigating the interfacial dynamics in the bulk chiral active models. In particular, we derive the stochastic partial differential equation
(SPDE) describing the dynamics of a fluctuating chiral interface with up-down symmetry
in one-dimension. The obtained SPDE has been studied before, and the
result on logarithmic corrections to scaling is stated in the Comment by Paczuski et al. However, the derivation from a bulk field theory is new, and the renormalisation
group calculation is unavailable in the literature. We derive the SPDE from an active field
theory for a non-conserved pseudoscalar field in a uniaxial medium equation, governing
the interfacial dynamics separating regions of opposite chirality. This dynamics turns
out to be equivalent to that of a steadily forced polymer. The steady-state probability
distribution of the one-dimensional shape of the domain wall is the same as the passive
Edwards-Wilkinson model. However, surprisingly, the dynamical behaviour of the
domain wall shape reveals its activity. A nonlinearity – which by scaling arguments is
marginal in one dimension – turns out to lead to anomalous growth. We examine this
numerically and analytically using a two-loop RG calculation to obtain the exponent
of the logarithmic correction to diffusivity.
The chapter 5 is on analytical modelling of experiments on AC field-driven Janus colloids in confined nematics. Electrokinetics involves study of electrically driven fluid
flow (electro-osmosis) and particle motion (electrophoresis). The use of electric fields to transport tiny particles through fluids, is an important technology
for macro-molecular sorting, colloidal assembly and a challenging area of soft-matter
research. Traditional studies on Electro-osmosis have been on colloids sus-
pended in isotropic electrolytes. Janus colloids in an isotropic electrolyte – with
dielectric and conducting hemispheres – show unidirectional motility (dielectric forward)
– thanks to the contrasting polarisability on the either hemispheres. However, this
phenomenon is unsuitable for self-assembly and micro-botic applications for its unidirec-
tional motion and eventual sedimentation in an isotropic electrolyte. In a striking depar-
ture from conventional electrophoresis, the experiments show that metal-dielectric
Janus particles can be piloted at will through a nematic liquid crystal film, in the plane
spanned by the axes of the particle and the nematic, and perpendicular to an imposed
AC electric field. A complete command over particle trajectories can be achieved by
varying field amplitude and frequency, exploiting the sensitivity of electro-osmotic flow
to the asymmetries of particle and defect structure. To understand the multi-directional
motility of janus particles in the experiments, we calculate the dipolar force density pro-
duced by the interplay of the electric field with director anchoring and the contrasting
electrostatic boundary conditions on the two hemispheres of the janus colloid to account
for the dielectric-forward (metal-forward) motion of the colloids due to induced puller
(pusher) force dipoles.
In the final chapter, we study Toner-Tu flocking on curved substrates. We
study the dynamics of density and polarisation fields on toroidal substrates and analytically calculate the steady-state profile. The Euler characteristic of the torus is zero and
hence defect-free states can exist which are well defined globally. We observe the density
profile to be inhomogeneous due to the presence of curvature. We also find delocalisa-
tion of extremas of density and polarity field. Further, the active flow allows the system
to have long-wavelength propagating sound modes which are gapped by the curvature,
while the gapless modes get localized to two special geodesics located on the positively and negatively curved faces.Raman-Charpak Fellowship of CEFIPR
Interaction of distinguished varieties and the Nevanlinna-Pick interpolation problem in some domains
No full textThis thesis explores the interplay between complex geometry and operator theory, focusing on characterizing certain objects from algebraic geometry. Two concepts that have
been of prime importance in recent times in the analysis of Hilbert space operators are
distinguished varieties, which are a priori geometric in nature, and joint spectra, which
are a priori algebraic in nature. This thesis brings them together to characterize all
distinguished varieties with respect to the bidisc, more generally the polydisc and the
symmetrized bidisc in terms of the joint spectrum of certain linear pencils. Some of the
results are shown to refine earlier work in these directions. The binding force is provided
by an operator-theoretic result, the Berger-Coburn-Lebow characterization of a tuple of
commuting isometries.
The thesis then turns to studying the uniqueness of solutions of the solvable NevanlinnaPick interpolation problems on the symmetrized bidisc and its connection with distinguished varieties. Several sucient conditions have been identified for a given data to
have a unique solution. Moreover, for a class of solvable data on the symmetrized bidisc,
there exists a distinguished variety where all solutions agree. Additionally, the thesis
explores the more general concept of the determining sets
Silk-based Biomaterials for Wound Care and Tissue Regeneration
No full textFor most individuals, wound healing is a highly organized, straightforward process. However, there are instances where external intervention becomes necessary to support the body’s innate healing mechanism. In this thesis, four such unmet clinical challenges were identified: rapid blood clotting, personalized treatment of burns and chronic wounds, and stretchable implants. Herein, we present novel solutions utilizing silk protein in various formats, each serving a distinct purpose in its respective application. Silk protein (silk fibroin) is being leveraged as a promising biomaterial with potent wound-healing activity. The first experimental chapter describes efforts to develop a potent hemostat for hemorrhage control. The primary goal was to develop a first-aid product for use in a pre-hospital setting where professional healthcare providers are not readily available (such as for battlefield injuries, road accidents, etc.). Herein, a bilayered hemostatic foam was designed such that the top bioactive layer served as a tissue interfacial layer to minimize rebleeding without compromising the clotting abilities. The subsequent two chapters describe strategies for personalized treatment of difficult-to-heal wounds: burns and chronic wounds. It is crucial to recognize that every patient and wound type is unique and requires individualized attention and care. To this end, two dressing materials were developed: a hydrogel-based dressing for burns and a multifunctional bioceramic-based drug delivery platform for chronic wounds. These dressing materials were specially designed for point-of-care applications and personalized treatment. Notably, the in vivo studies revealed the superior healing efficacy of the burn dressing compared to the commercially available product. Moreover, the multifunctional bioceramic-based product exhibited promising antioxidant and antibacterial properties, making it a potential candidate for chronic wounds. The last part of the thesis introduces ultra-stretchable 3D printed biocompatible hydrogels. Herein, a ternary blend ink was carefully formulated for extrusion-based 3D printing. The developed hydrogel presented superior mechanical properties, including good stretchability and fatigue performance. These mechanically robust hydrogels have potential applications in stretchable implants, bioelectronics, and flexible wearables. This thesis was accomplished through a collaborative effort with Fibroheal Woundcare Pvt. Ltd., a startup based in Bangalore, India. Some products developed within the scope of this thesis are in the process of being commercialized. With the translation of these advancements into the market, we envision that technologies will be available in the clinic to alleviate clinical challenges for improved patient care
Constrained Stochastic Differential Equations on Smooth Manifolds.
No full textDynamical systems with uncertain fluctuations are usually modelled using Stochastic Differential Equations (SDEs). Due to operation and performance related conditions, these equations may also need to satisfy the constraint equations. Often the constraint equations are ``algebraic". Such constraint equations along with the given SDE form a system of Stochastic Differential-Algebraic Equations (SDAEs).
The main objective of this thesis is to consider these equations on smooth manifolds. However, we first consider SDAEs on Euclidean spaces to understand these equations locally. A sufficient condition for the existence and uniqueness of the solution is obtained for SDAEs on Euclidean spaces. We also give necessary condition for the existence of the solution. Based on the necessary condition, there exists a class of SDAEs for which there is no solution. Since all SDAEs are not solvable, we present methods and algorithms to find approximate solution of the given SDAE.
In order to extend this work to smooth manifolds, we consider second order stochastic differential geometry to construct Schwartz morphism to represent SDEs with drift that are driven by p-dimensional Wiener process. We show that it is possible to construct such Schwartz morphisms using what we call as \textit{diffusion generators}. We demonstrate that diffusion generator can be constructed using flow of second order differential equations, in particular using regular Lagrangians. The results obtained for SDAEs on Euclidean spaces are extended to SDAEs on smooth manifolds using the framework of diffusion generators. We show that the results obtained for SDAEs on Euclidean spaces translate to the manifold setting with minimal modifications. We have derived Ito-Wentzell's formula on manifolds in the framework of diffusion generators to obtain approximate bounded solution with unit probability. Another type of approximate solution is bounded solution such that the probability of explosion is bounded by . We present algorithms to compute approximate solutions of both type. This has been demonstrated with an example of SDAE on a sphere