arXiv subjects
Publications and source records attributed to Manish Kumar.
In this paper we investigate the primeness of a class of entire functions and discuss the dynamics of a periodic member f of this class with respect to a transcendental entire function g that permutes with f. In particular we show that the Julia sets of f and g are identical.
Recent success in synthesizing thermally stable nanofluids at low costs is a significant breakthrough in the evolution of volumetric absorption based solar thermal systems. However, we have yet not been able to clearly identify the range of operating and design parameters in which volumetric absorption could prove to be beneficial. One of the key reasons being that we have not been able to fully understand the heat transfer mechanisms involved in these novel systems. The present work takes a few steps further in this direction wherein we have developed a comprehensive and mechanistic theoretical framework which is robust enough to account for coupled transport phenomena and orders of magnitudes of operating parameters for host of receiver design configurations. Moreover, we have also modeled equivalent surface absorption based systems to provide a comparison between volumetric and surface absorption processes under similar operating conditions. Performance characteristics reveal that particularly at high solar concentration ratios, volumetric absorption-based receivers could have 35% - 49% higher thermal efficiencies compared to their surface absorption-based counterparts. Finally, the present work serves to define optimal performance domains of these solar thermal systems, particularly in the laminar flow regime (200 < Re < 1600) and over a wide range of solar concentration ratios (5-100) and inlet fluid temperatures (293-593K).
This Letter presents the first demonstration of multi-tile stitching for large scale 3D imaging in single objective light-sheet microscopy. We show undistorted 3D imaging spanning complete zebrafish larvae, and over 1 mm3 volumes for thick mouse brain sections. We use remote galvo scanning for light-sheet creation and develop a processing pipeline for 3D tiling across different axes. With the improved one photon (1p) tilt-invariant scanned oblique plane illumination (SOPi) microscope presented here, we demonstrate cellular resolution imaging at depths exceeding 330 um in optically scattering mouse brain samples, and dendritic imaging in more superficial layers.
We numerically and experimentally investigate evaporation of a sessile droplet on a heated substrate. We develop a finite element (FE) model in two-dimensional axisymmetric coordinates to solve coupled transport of heat in the droplet and substrate, and of the mass of liquid vapor in surrounding ambient while assuming diffusion-limited, quasi-steady evaporation of the droplet. The two-way coupling is implemented using an iterative scheme and under-relaxation is used to ensure numerical stability. The FE model is validated against the published spatial profile of the evaporation mass flux and temperature of the liquid-gas interface. We discuss cases in which the two-way coupling is significantly accurate than the one-way coupling. In experiments, we visualized side view of an evaporating microliter water droplet using a high-speed camera at different substrate temperatures and recorded temperature of the liquid-gas interface from the top using an infrared camera. We examine the dependency of inversion of the temperature profile across the liquid-gas interface on the ratio of the substrate thickness to the wetted radius, the ratio of the thermal conductivity of the substrate to that of the droplet and contact angle. A comparison of measured evaporation mass rate with the computed values at different substrate temperature show that the evaporation mass rate increases non-linearly with respect to the substrate temperature, and FE model predicts these values close to the experimental data. Comparisons of time-averaged evaporation mass rate obtained by the previous and present models against the measurements suggest that the evaporative cooling at the interface and variation of diffusion coefficient with temperature should be taken into account in the model in order to accurately capture the measurements.
Zero field cooled spontaneous exchange bias (SEB) is observed in epitaxial La0.7Sr0.3MnO3 (LSMO):NiO self-assembled nanocomposite thin films grown on (001) SrTiO3 single crystal substrate by pulsed laser deposition. SEB is displayed by the novel asymmetry in the hysteresis loop of the composite film along with the field cooled conventional exchange bias (CEB) effect. The training effect shows that exchange bias relaxation is disorder mediated. It is revealed from DC magnetization results that such nanocomposite film divulges spin glass like behaviour, which is arising due to competing ferromagnetic and antiferromagnetic inteactions at the assorted interfaces of ferromagnetic LSMO and antiferromagnetic NiO. Also corroborated by x-ray magnetic circular dichroism (XMCD) measurements, we conclude that SEB is mainly originating due to ferromagnetic coupling of unstable interfacial antiferromagnetic spin due to NiO with the ferromagnetic LSMO at the disordered interface. These results of self-assembled thin films provide a useful input to realize and understand microscopic origin of SEB for device application.
The wild part of Abhyankar's Inertia Conjecture for a product of certain Alternating groups is shown for any algebraically closed field of odd characteristic. For $d$ a multiple of the characteristic of the base field, a new étale $A_d$-cover of the affine line is obtained using an explicit equation and it is shown that it has the minimal possible upper jump.
Versatile, sterically accessible imaging systems capable of in vivo rapid volumetric functional and structural imaging deep in the brain continue to be a limiting factor in neuroscience research. Towards overcoming this obstacle, we present integrated one- and two-photon scanned oblique plane illumination (SOPi) microscopy which uses a single front-facing microscope objective to provide light-sheet scanning based rapid volumetric imaging capability at subcellular resolution. Our planar scan-mirror based optimized light-sheet architecture allows for non-distorted scanning of volume samples, simplifying accurate reconstruction of the imaged volume. Integration of both one-photon (1P) and two-photon (2P) light-sheet microscopy in the same system allows for easy selection between rapid volumetric imaging and higher resolution imaging in scattering media. Using SOPi, we demonstrate deep, large volume imaging capability inside scattering mouse brain sections and rapid imaging speeds up to 10 volumes per second in zebrafish larvae expressing genetically encoded fluorescent proteins GFP or GCaMP6s. SOPi flexibility and steric access makes it adaptable for numerous imaging applications and broadly compatible with orthogonal techniques for actuating or interrogating neuronal structure and activity.
Formal orbifolds are defined in higher dimension. Their étale fundamental groups are also defined. It is shown that the fundamental groups of formal orbifolds have certain finiteness property and it is also shown that they can be used to approximate the étale fundamental groups of normal varieties. Etale site on formal orbifolds are also defined. This framework allows one to study wild ramification in an organised way. Brylinski-Kato filtration, Lefschetz theorem for fundamental groups and $l$-adic sheaves in these contexts are also studied.
Algebraic parabolic bundles on smooth projective curves over algebraically closed field of positive characteristic is defined. It is shown that the category of algebraic parabolic bundles is equivalent to the category of orbifold bundles defined in \cite{KP}. Tensor, dual, pullback and pushforward operations are also defined for parabolic bundles.
We introduce a practical digital holographic method capable of imaging through a diffusive or scattering medium. The method relies on statistical averaging from a rotating ground glass diffuser to negate the adverse effects caused by speckle introduced by a first, static diffuser or scattering medium. In particular, a setup based on Fourier transform holography is used to show that an image can be recovered after scattering by introducing an additional diffuser in the optical setup. This method is capable of recovering object information from behind a scattering layer in biomedical or military imaging applications.
We present a new, single step approach for generating a hexagonal lattice wave-field with a gradient local basis structure. We incorporate this by coherently superposing two (or more) hexagonal lattice wave-fields which differ in their basis structures. The basis of the resultant lattice wave-field is highly dependent on the relative strengths of constituent wave-fields and a desired spatial modulation of basis structure is thus obtained by controlling the spatial modulation of relative strengths of constituent wave-fields. The experimental realization of gradient lattice is achieved by using a phase only spatial light modulator (SLM) in an optical 4f Fourier filter setup where the SLM is displayed with numerically calculated gradient phase mask. The presented method is wavelength independent and is completely scalable making it very promising for micro-fabrication of corresponding structures.
We propose a simple and straightforward method to generate a spatially variant lattice structures by optical interference lithography method. Using this method, it is possible to independently vary the orientation and period of the two-dimensional lattice. The method consists of two steps which are: numerical synthesis of corresponding phase mask by employing a two-dimensional integrated gradient calculations and experimental implementation of synthesized phase mask by making use of a phase only spatial light modulator in an optical 4f Fourier filtering setup. As a working example, we provide the experimental fabrication of a spatially variant square lattice structure which has the possibility to guide a Gaussian beam through a 90° bend by photonic crystal self-collimation phenomena. The method is digitally reconfigurable, is completely scalable and could be extended to other kind of lattices as well.
We present an experimental method based on a modified multiple beam interference approach to generate an optical vortex array arranged in a spatially varying lattice. This method involves two steps which are: numerical synthesis of a consistent phase mask by using two-dimensional integrated phase gradient calculations and experimental implementation of produced phase mask by utilizing a phase only spatial light modulator in an optical 4f Fourier filtering setup. This method enables an independent variation of the orientation and period of the vortex lattice. As working examples, we provide the experimental demonstration of various spatially variant optical vortex lattices. We further confirm the existence of optical vortices by formation of fork fringes. Such lattices may find applications in size dependent trapping, sorting, manipulation and photonic crystals.
We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their étale coverings and their fundamental groups are also defined. These fundamental group approximates the fundamental group of an appropriate affine curve. We also define vector bundles on these objects and the category of orbifold bundles on any smooth projective curve. Analogues of various statement about vector bundles which are true in characteristic zero are proved. Some of these are positive characteristic avatar of notions which appear in the second author's work ([Par]) in characteristic zero.
We present a technique to optically induce a defect site in helical lattice wave-field where the combined wave-field continues to maintain its nondiffracting (ND) nature. This is done by coherently superposing a helical lattice wave-field and a Bessel beam by method of phase engineering. The results are confirmed by numerical simulations and experimentally as well by generating the ND defect beam by displaying the numerically calculated phase pattern on a phase-only spatial light modulator. This technique is wavelength independent, completely scalable, and can easily be used to generate or transfer these structures in any photosensitive medium.
We present a method to combine two periodic lattice wave-fields to generate a complex dual lattice wave-field which could be employed for microfabrication of corresponding 2D dual lattice structures. Since the addition of two periodic lattice wave-fields is coherent in nature the resultant dual lattice structure is highly dependent on the relative phase difference between constituent wave-fields. We show that it is possible to have control over the dual lattice pattern by precisely controlling this relative phase difference. This control is enabled by making use of digitally addressable phase only spatial light modulator (SLM). We provide the computational method for calculation of corresponding phase mask to be displayed on the SLM and also verify the results experimentally by employing a simple 4f Fourier filter based geometry. The method is completely scalable and reconfigurable in terms of the choice of periodic lattice wave-fields and has the potential to form gradient phase masks which could be useful for fabrication of graded index optical components.
This work presents a smart trespasser detection and alert system which aims to increase the amount of security as well as the likelihood of positively identifying or stopping trespassers and intruders as compared to other commonly deployed home security system. Using multiple sensors, this system can gauge the extent of danger exhibited by a person or animal in or around the home premises, and can forward certain critical information regarding the same to home owners as well as other specified persons such as relevant security authorities.
In this work, we design and develop a smart intruder detection and alert system which aims to elevate the security as well as the likelihood of true positive identification of trespassers and intruders as compared to other commonly deployed electronic security systems. Using multiple sensors, this system can gauge the extent of danger exhibited by a person or animal in or around the home premises, and can forward various critical information regarding the event to home owners as well as other specified entities, such as relevant security authorities.