My research group has two broad areas of focus. One part of the research group has studied physics of spontaneous light emission and emitter-matter interactions to develop theoretical ideas and computational models. Our theoretical work is tested in man-made materials through our collaboration with experimental groups. The other area of interest includes methods for numerical and statistical computing. Our tools of analysis includes only working mathematics, to minimize abstraction even while trying to maximize generality. This work may combine mathematics and computational solutions as general-purpose methods for scientific/engineering problems. A short talk summarizing most of our recent research topics and its results can be found here. A longer talk on circulant decomposition of a matrix and its use in fast multiplication of large matrices is here.

Vita

• “The Book Under My Pillow”, Leadstart Publishing 2012  (US; India)
• “Science in the golden shackles of  its imaginary impacts”, June 2014.
• “Education in the information age: the science and the art in making up a mind,” for the Newsletter of Board for IT education standards (BITES) in Karnataka, Aug 2014.
• Emerging modi operandi in institutions for scientific research, Aug 2016.
• Bipartisanship of the voter is a first necessity in democracies, Jan 2017.


• IISc campus-calls : Bird Watch; more to come...

Computational & Statistical Physics Group

Considering our interests, research topics are diverse among members of this small group. Noting the ‘re’ in research, we like to retest, simplify and generalize the known science.

Methods for Numerical Computation & Statistical Estimation:

Advances in numerical methods have contributed to computing power as much as the developments in hardware resources over the last few decades. Our recent results include analysis of polynomial recurrence relations and fast computing methods for certain eigenvalue problems, circulant decomposition of a matrix, methods for sampling and estimation that may substitute Markov-Chain-Monte-Carlo (MCMC) methods, and error estimators for linear solvers. The topics in scientific computing included efficient approximations of spherical scattering coefficients, analysis of various approximations of the Sommerfeld integrals, and efficient generation of random directions in high-D cones with uniform probability density. Our work is demonstrated as usable algorithms, either with bounds on convergence or a statistical performance analysis over numerous problems.

Emitter-Matter interaction and its Physics:

Understanding effects of size of a structure on its intrinsic optical properties, and coupling between emitters and nanoscale structures are areas of interest. These theoretical and numerical studies in turn help us understand the limits of the current models of emission or absorption, and find ways to enhance that efficiency in materials. Our recent results include a computational method for quantum N-body problems of emission in nanoscale materials, and modifications in the theory for strong matter-coupling regime of spontaneous emission.

Applied Optics & Computation:

In the past, we have used models to develop composite nanoparticles and nanostructures that have counterintuitive but useful properties. We have studied absorption, chiral and directional scattering properties of nanostructures with applications in mind.  These works involved active experimentation in collaboration with experimental groups in campus and with our industrial partners.

Publications

Note: Copyrights of these articles (by Muru Venkatapathi and his collaborators/students) are with the publishers / authors.  These articles may be downloaded only for personal use. Any other use requires prior explicit permission of the authors and the publisher.

Solemn Declaration: 1) We will send articles for review/print only if we think our work significantly alters/extends/simplifies current understanding of the Science and 2) We will not claim novelty in our manuscripts using any wilful embellishments of a literary, graphical, or algebraic nature.  We realize that the peer-review system is severely stressed and deformed by its own weight, and that there is a misplaced emphasis on our rudimentary citation system which might be fast losing its correlation to the real impacts of Science. So it is our responsibility to make an effort; see related article by MV.

• An O(n) algorithm for generating uniform random vectors in n-dimensional cones (Arun I.).Preprint
• Circulant decomposition of a matrix and the eigenvalues of Toeplitz type matrices (Hariprasad M.), Applied Mathematics & Computation 468, 128473 (2024).Preprint
• Emission enhancement in nanoassemblies with extremely small metal nanoparticles: Nonmonotonic effect of temperature and the non-Markovian interactions (R. Dutta, K. Jain, K. Sharma and J. K. Basu), Physical Review Materials 7, 105201 (2023).
• An algorithm for estimating non-convex volumes and other integrals in n dimensions (Arun I. and Abhijeet J.), Computational & Applied Mathematics 42, 242 (2023).Print
• Approximations for spherical scattering coefficients with negligible integral errors in parametric space (A. Khan), J. Opt. Soc. Amer. A 40 (5), 932-941 (2023).Preprint
• Error estimators and their analysis for CG, Bi-CG and GMRES (P. Jain and K. Manglani), Numerical Analysis & Applications 16 (2), 135–153 (2023).Preprint
• Radiative decay of an emiter due to non-Markovian interactions with dissipating matter (K. Jain), J. Physics:Condensed Matter 132, 113103 (2022).Preprint
• Role of Rabi oscillations in radiative states due to the fully absorbing smaller plasmonic nanoparticles (K. Jain), J. Applied Physics 132, 113103 (2022).Preprint
• Semi-analytical solutions for eigenvalue problems of chains and periodic graphs (Hariprasad M.), Applied Mathematics & Computation 411, 126512 (2021).Preprint
• Large emission enhancement and emergence of strong coupling with plasmons in nanoassemblies: Role of quantum interactions and finite emitter size (R. Dutta, K. Jain and J. K. Basu), Physical Review B 100, 155413 (2019). PDF
• Strong coupling of an emitter with absorbing matter : A regime for enhancement of light emission (K. Jain), Physical Review Applied 11, 054002 (2019). PDF
• Signal Enhancement from Tunable SERS Substrates: Design and Demonstration of Multiple Regimes of Enhancement (D. R. Nayak, N. Bhat and S. Umapathy), J. Physical Chemistry C 122 (16),  9134–9140 (2018). PDF
• Fano-type spectra and other interference effects in an all-dielectric nanoshell (S. Garg), J. Optics 19, 075603 (2017). PDF
• Impact of ultrathin dielectric spacers on SERS: energy transfer between polarized charges and plasmons (D. R. Nayak, N. Bhat and S. Umapathy), J. Material Chemistry C 5, 2123-2129 (2017). PDF
• Analysis of numerical solutions to Sommerfeld integral relation of the half-space radiator problem (Arun I.), Applied Numerical Mathematics 106, 79-97 (2016). PDF
• Plasmon-mediated emergence of collective emission and enhanced quantum efficiency in quantum dot films (Praveena M., A. Mukherjee & J. K. Basu), Physical Review B 92, 235403 (2015). PDF
• Collective eigenstates of emission in an N-entity heterostructure and the evaluation of its Green tensors and self-energy components, J. Opt. Soc. Amer. B 31, 3153-3163 (2014). PDF
• Plasmonic interactions at close proximity in chiral geometries: Route towards broadband chiroptical response and giant enantiomeric sensitivity (G. Nair, H. S. Johnson, D. Paria & A. Ghosh), J. Physical Chemistry C 118, 4991–4997 (2014). PDF
• Photoluminescence decay rate engineering of CdSe quantum dots in ensemble arrays embedded with gold nano-antennae (M. Haridas, A. K. Tiwari & J. K. Basu), J. Applied Physics 114, 064305 (2013). PDF
• Enhanced photo-absorption efficiency of incomplete nanoshells (S. G. Dastidar, P. Bharath, A. Roy & A. Ghosh), Optics Letters 38, 3275-3278 (2013). PDF
• Radiative and non-radiative effects of a substrate on localized plasmon resonance of particles (A. K. Tiwari), J. Applied Physics 112, 013529 (2012).  PDF
• Emitter near an arbitrary body: Purcell effect, optical theorem and the Wheeler-Feynman absorber, J. Quant. Spectros. Radiat. Transfer 113, 1705–1711 (2012). PDF


Other technical reports, proceedings and upublished thesis work:


• Reliability of citation count in predicting scientific impact : an estimation using higher order citation indices (Naga N. G.).PDF
• Matrix multiplication using the circulant decomposition (Sai Gowri J. N.).PDF
• Semi-analytical solution for eigenvalue problems of lattice models with boundary conditions (Athira G.).PDF
• An Analysis of the Human Development Index and Modelling Income Distributions (Prajakta B. Sanjay).PDF
• An Analysis of the Limitations of University Rankings and Its Use (Lubhawan P.).PDF
• A short study comparing countries on the quality of response to the Covid-19 pandemic (Thilakam V.).PDF
• Numerical Analysis of Some Preconditioners and Associated Error Estimators for Solving Linear Systems (Abhishek D.).PDF
• Calculation of the extinction cross section and lifetime of a gold nanoparticle using FDTD simulations (Archana R.).PDF
• Enhancement of scattering from nanoparticles using substrate effect (K. Chakraborty, A. Tiwari and M. Varma).PDF