arXiv subjects

R. Krishnan

Publications and source records attributed to R. Krishnan.

At least 19 recordsLinked to original sources

arXiv2023

Homogeneous linear intrinsic constraints in the stationary manifold of a $G$-invariant potential

Given a $G$-invariant potential $\mathcal{V}$ of a scalar multiplet $φ$, there may exist a set of homogenous linear equations that constrain the components of a stationary point of $\mathcal{V}$ independently of the coefficients of the terms in $\mathcal{V}$. We call them homogeneous linear intrinsic constraints (HLICs). HLICs in a stationary point manifest as HLICs in the corresponding vacuum alignment of $φ$, which plays a central role in predictive phenomenological models. We discover that a group $\tilde{H}$ generates HLICs if the terms in $\mathcal{V}$ satisfy a condition, which we call the compatibility condition. In this paper, we also develop a procedure, which involves splitting $\mathcal{V}$ into smaller parts, to establish the existence of specific stationary points using arguments based on symmetries without the need for explicitly extremizing the potential. Using this procedure, we obtain $\tilde{H}$ as a direct product of the symmetry groups associated with the various irreducible multiplets (irreps) in $φ$. This results from considering the potentials of the irreps separately and verifying if the cross terms are compatible with $\tilde{H}$.

hep-ph↗

arXiv2023

The framework of the auxiliary group: two birds with one stone

Flavon models in the literature assume constraints on the components of the vacuum expectation values (vevs) of flavons, and typically, these constraints are not fully determined by the residual symmetry group of the set of vevs. This poses a problem because the general potential of the flavons cannot have a minimum that leads to such constraints unless additional mechanisms involving supersymmetry, extra dimensions etc., are invoked. In this paper, we show that the framework of the auxiliary group naturally results in vevs satisfying the required constraints, and using it, we construct a type-1 seesaw model with two right-handed neutrinos, which predicts the ratio of the light neutrino masses $m_2/m_3=(\sqrt{2}-1)/(\sqrt{2}+1)$ and $\text{TM}_1$ mixing with $\sinθ_{13}=\frac{1}{\sqrt{3}}\sin\fracπ{12}$ and $\sinδ_\text{CP}=-1$. Our framework posits auxiliary group transformations which act on the flavons but not on the fermions. We construct the general renormalizable potential without invoking additional mechanisms and show that it has a minimum that leads to the required constraints.

hep-ph↗

arXiv2023

Understanding the soil water dynamics during excess and deficit rainfall conditions over the Core monsoon zone of India

Observations of soil moisture (SM) during excess and deficit monsoon seasons between 2000 to 2021 present a unique opportunity to understand the soil water dynamics (SWD) over core monsoon zone (CMZ) of India. This study aims to analyse SWD by investigating the SM variability, SM memory (SMM), and the coupling between the surface and subsurface SM levels. Particularly intriguing are instances of concurrent monsoonal extremes, which give rise to complex SWD patterns. Usually, it is noted that a depleted convective activity and persistence of higher temperatures during the pre-monsoon season leads to lower SM, while monsoon rains and post-monsoon showers support the prevalence of higher SM conditions. The long persistent dry spells during deficit monsoon years enhances the Bowen ratio (BR) due to the high sensible heat fluxes. On the other hand, the availability of large latent heat flux during excess monsoon and post-monsoon seasons tends to decrease the BR. This enhancement or reduction in BR is due to evapotranspiration (ET), which influences the SWD by modulating the surface subsurface SM coupling. The surface and subsurface SM coupling analysis for CMZ exhibits significant distinction in the evolution of wet and dry extremes. SM variations and persistence time scale is used as an indicator of SMM, and analysed for both surface and subsurface SM observation levels. Evidently, subsurface SM exhibits remarkably prolonged memory timescales, approximately twice that of surface SM. Furthermore, we dissect SWD linked to wet and dry extremes by analysing annual soil water balance (SWB). Our findings reveal augmented (diminished) ET during deficit (excess) years, subjected to a higher (lower) number of break events. In essence, our study underscores the significance of surface-subsurface SM observations in unravelling the intricate tapestry of SWD.

physics.ao-ph↗

arXiv2022

Experimental study to optimise the treatment efficacy of pharmaceutical effluents by combining electron beam irradiation with conventional techniques

The inability of conventional methods to completely remove the contaminants from pharmaceutical effluents led us to study the effect of Electron Beam (EB) irradiation on real pharmaceutical wastewater. In this paper, the samples from different stages of existing treatment facilities of industry are irradiated with varying doses from 25 to 200 kGy. The study aimed to find a suitable combination of EB and conventional treatments for efficient degradation of complex pharmaceutical effluent. It has been successfully demonstrated that electron beam irradiation when combined with conventional techniques like coagulation before or after the irradiation improves the efficiency of the process, resulting in lower Chemical Oxygen Demand (COD). In this investigation, the maximum COD reduction was found to be around 65 percent.

physics.bio-ph↗

arXiv2021

The IITM Earth System Model (IITM ESM)

Earth System Models (ESM) are important tools that allow us to understand and quantify the physical, chemical & biological mechanisms governing the rates of change of elements of the Earth System, comprising of the atmosphere, ocean, land, cryosphere and biosphere (terrestrial and marine) and related components. ESMs are essentially coupled numerical models which incorporate processes within and across the different Earth system components and are expressed as set of mathematical equations. ESMs are useful for enhancing our fundamental understanding of the climate system, its multi-scale variability, global and regional climatic phenomena and making projections of future climate change. In this chapter, we briefly describe the salient aspects of the Indian Institute of Tropical Meteorology ESM (IITM ESM), that has been developed recently at the IITM, Pune, India, for investigating long-term climate variability and change with focus on the South Asian monsoon.

physics.ao-ph↗

arXiv2020

Future Climate Change Projections over the Indian Region

Assessments of impacts of climate change and future projections over the Indian region, have so far relied on a single regional climate model (RCM) - eg., the PRECIS RCM of the Hadley Centre, UK. While these assessments have provided inputs to various reports (e.g., INCCA 2010; NATCOMM2 2012), it is important to have an ensemble of climate projections drawn from multiple RCMs due to large uncertainties in regional-scale climate projections. Ensembles of multi-RCM projections driven under different perceivable socio-economic scenarios are required to capture the probable path of growth, and provide the behavior of future climate and impacts on various biophysical systems and economic sectors dependent on such systems. The Centre for Climate Change Research, Indian Institute of Tropical Meteorology (CCCR-IITM) has generated an ensemble of high resolution downscaled projections of regional climate and monsoon over South Asia until 2100 for the Intergovernmental Panel for Climate Change (IPCC)using a RCM (ICTP-RegCM4) at 50 km horizontal resolution, by driving the regional model with lateral and lower boundary conditions from multiple global atmosphere-ocean coupled models from the Coupled Model Intercomparison Project Phase 5 (CMIP5). The future projections are based on three Representation Concentration Pathway (RCP) scenarios (viz., RCP2.6, RCP4.5, RCP8.5) of the IPCC.

physics.ao-ph↗

arXiv2020

Regional Climate Change Datasets for South Asia

The Centre for Climate Change Research (CCCR;http://cccr.tropmet.res.in) at the Indian Institute of Tropical Meteorology (IITM; http://www.tropmet.res.in), Pune, launched in 2009 with the support of the Ministry of Earth Sciences (MoES), Government of India, focuses on the development of new climate modelling capabilities in India and South Asia to address issues concerning the science of climate change. CCCR-IITM has the mandate of developing an Earth System Model and to make the regional climate projections. An important achievement was made by developing an Earth System Model at IITM, which is an important step towards understanding global and regional climate response to long-term climate variability and climate change. CCCR-IITM has also generated an ensemble of high resolution dynamically downscaled future projections of regional climate over South Asia and Indian monsoon, which are found useful for impact assessment studies and for quantifying uncertainties in the regional projections. A brief overview of these core climate change modeling activities of CCCR-IITM was presented in an Interim Report on Climate Change over India (available at http://cccr.tropmet.res.in/home/reports.jsp)

physics.ao-ph↗

arXiv2020

A short perspective on the Mascarene High and the abnormal Indian Monsoon during 2015

The initiation of the Indian summer monsoon circulation during late May / early June arises through large-scale land-sea thermal contrast and setting up of negative pressure gradient between the Monsoon Trough over the Indo-Gangetic plains and the Mascarene High over the subtropical Indian Ocean. The meridional pressure gradient together with the Earth's rotation (Coriolis force) creates the summer monsoon cross-equatorial flow, while feedbacks between moisture-laden winds and latent heat release from precipitating systems maintain the monsoon circulation during the June-September (JJAS) rainy season (Krishnamurti and Surgi, 1987). This simplified view of the Indian monsoon is a useful starting point to draw insights into the variability of the large-scale monsoon circulation.

physics.ao-ph↗

arXiv2020

Effect of sterile neutrino on low energy processes in minimal extended seesaw with $Δ(96)$ symmetry and $\text{TM}_{1}$ mixing

We study the effect of sterile neutrino on some low scale processes in the framework of minimal extended seesaw (MES). MES is the extension of the seesaw mechanism with the addition of sterile neutrino of intermediate mass. The MES model in this work is based on $Δ(96)\times C_{2}\times C_{3}$ flavor symmetry. The structures of mass matrices in the framework lead to $TM_{1}$ mixing with $μ\text{-}τ$ symmetry. The model predicts maximal value of Dirac CP phase. We carry out our analysis to study the new physics contributions from the sterile neutrino to different charged lepton flavor violation (cLFV) processes involving muon and tau leptons as well as neutrinoless double beta decay (0$νββ$). The model predicts normal ordering (NO) of neutrino masses and we perform the numerical analysis considering normal ordering (NO) only. We find that sterile neutrino mass in GeV range can lead to cLFV processes that are within the reach of current and planned experiments. The GeV scale sterile neurtrino in our model is consistent with the current limits on the effective neutrino mass set by $0νββ$ experiments.

hep-ph↗

arXiv2020

Realization of the minimal extended seesaw mechanism and the $TM_2$ type neutrino mixing

We construct a neutrino mass model based on the flavour symmetry group $A_4\times C_4 \times C_6 \times C_2$ which accommodates a light sterile neutrino in the minimal extended seesaw (MES) scheme. Besides the flavour symmetry, we introduce a $U(1)$ gauge symmetry in the sterile sector and also impose CP symmetry. The vacuum alignments of the scalar fields in the model spontaneously break these symmetries and lead to the construction of the fermion mass matrices. With the help of the MES formulas, we extract the light neutrino masses and the mixing observables. In the active neutrino sector, we obtain the $\text{TM}_2$ mixing pattern with non-zero reactor angle and broken $μ$-$τ$ reflection symmetry. We express all the active and the sterile oscillation observables in terms of only four real model parameters. Using this highly constrained scenario we predict $\sin^2 θ_{23} =0.545^{+0.003}_{-0.004}$, $\sin δ= -0.911^{+0.006}_{-0.005}$, $|U_{e4}|^2 = 0.029^{+0.009}_{-0.008}$, $|U_{\mu4}|^2 = 0.010^{+0.003}_{-0.003}$ and $|U_{\tau4}|^2 = 0.006^{+0.002}_{-0.002}$ which are consistent with the current data.

hep-ph↗

arXiv2020

Meta Continual Learning via Dynamic Programming

Meta continual learning algorithms seek to train a model when faced with similar tasks observed in a sequential manner. Despite promising methodological advancements, there is a lack of theoretical frameworks that enable analysis of learning challenges such as generalization and catastrophic forgetting. To that end, we develop a new theoretical approach for meta continual learning~(MCL) where we mathematically model the learning dynamics using dynamic programming, and we establish conditions of optimality for the MCL problem. Moreover, using the theoretical framework, we derive a new dynamic-programming-based MCL method that adopts stochastic-gradient-driven alternating optimization to balance generalization and catastrophic forgetting. We show that, on MCL benchmark data sets, our theoretically grounded method achieves accuracy better than or comparable to that of existing state-of-the-art methods.

cs.LG↗

arXiv2020

Predictive $S_4$ flavon model with $\text{TM}_1$ mixing and baryogenesis through leptogenesis

We use $S_4$ discrete group to construct a neutrino flavour model which leads to $TM_1$ mixing and is consistent with the neutrino oscillation data. Using the model's constrained parameter space, we predict the values of Dirac $CP$ phase and the light neutrino mass as $-1<\sin δ<-0.9$ and $1.7<m_1 (\text{meV})<5.5$ respectively. We thoroughly examine the usefulness of this model in explaining the observed baryon asymmetry of the Universe. Near-maximal breaking of CP symmetry (arising due to the $\text{TM}_1$ constraint) helps us in generating adequate baryon asymmetry through leptogenesis. We study the evolution of the asymmetry (generated due to the decay of the heavy Majorana neutrinos) starting from the primordial Universe in two different ways (i)explicitly solving network of Boltzmann equations, (ii) using approximate analytic solution and we have shown the extent of their equivalence. Nearly accurate analytical fits are used thereafter to evaluate baryon asymmetry for the whole parameter space allowed by $3σ$ global fit of oscillation data and to impose a constraint on the yet unbounded mass scale parameter of Dirac neutrino mass matrix. Furthermore, significant contribution of $N_2$ decay in the context of flavoured leptogenesis is also estimated.

hep-ph↗

arXiv2020

Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?

In the framework of the representation theory of finite groups, it was recently shown that a fully constrained complex-symmetric mass matrix can be conveniently mapped into a sextet of $Σ(72\times3)$. In this paper, we introduce an additional flavor group $X_{24}$ in the model so that the vacuum alignment of the $Σ(72\times3)$ sextet is determined not only by the symmetries of $Σ(72\times3)$ but also by that of $X_{24}$. We define several flavons which transform as multiplets under $Σ(72\times3)$ as well as $X_{24}$. The vacuum alignment of each of these flavons is obtained as a simultaneous invariant eigenstate of specific elements of the groups $Σ(72\times3)$ and $X_{24}$; i.e.,~the vacuum alignment is fully determined by its residual symmetries. These flavons couple together uniquely resulting in the fully constrained sextet of $Σ(72\times3)$. Through this work we propose a general formalism in which the flavor symmetry group ($G_f$) is obtained as the direct product, $G_f=G_r \times G_x$. Fermions transform nontrivially only under $G_r$ while they remain invariant under $G_x$. Flavons, on the other hand, transform nontrivially under both $G_r$ and $G_x$. The vacuum alignment of each flavon multiplet transforming irreducibly under $G_r \times G_x$ is uniquely identified by its corresponding residual symmetry (a subgroup of $G_r \times G_x$). Several such flavons couple together to form an effective multiple of $G_r$ which remains invariant under $G_x$. This effective multiplet couples to the fermions.

hep-ph↗

arXiv2018

Fully Constrained Majorana Neutrino Mass Matrices Using $Σ(72\times 3)$

In 2002, two neutrino mixing ansatze having trimaximally-mixed middle ($ν_2$) columns, namely tri-chi-maximal mixing ($\text{T}χ\text{M}$) and tri-phi-maximal mixing ($\text{T}ϕ\text{M}$), were proposed. In 2012, it was shown that $\text{T}χ\text{M}$ with $χ=\pm \fracπ{16}$ as well as $\text{T}ϕ\text{M}$ with $ϕ= \pm \fracπ{16}$ leads to the solution, $\sin^2 θ_{13} = \frac{2}{3} \sin^2 \fracπ{16}$, consistent with the latest measurements of the reactor mixing angle, $θ_{13}$. To obtain $\text{T}χ\text{M}_{(χ=\pm \fracπ{16})}$ and $\text{T}ϕ\text{M}_{(ϕ=\pm \fracπ{16})}$, the type~I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, $m_1:m_2:m_3=\frac{\left(2+\sqrt{2}\right)}{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left(2+\sqrt{2}\right)}{-1+\sqrt{2(2+\sqrt{2})}}$. In this paper we construct a flavour model based on the discrete group $Σ(72\times 3)$ and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric $3\times 3$ matrix with 6 complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex 6 dimensional representation of $Σ(72\times 3)$. Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.

hep-ph↗

arXiv2016

The SU(3) Algebra in a Cyclic Basis

With the couplings between the eight gluons constrained by the structure constants of the su(3) algebra in QCD, one would expect that there should exist a special basis (or set of bases) for the algebra wherein, unlike in a Cartan-Weyl basis, {\em all} gluons interact identically (cyclically) with each other, explicitly on an equal footing. We report here particular such bases, which we have found in a computer search, and we indicate associated $3 \times 3$ representations. We conjecture that essentially all cyclic bases for su(3) may be obtained from these making appropriate circulant transformations,and that cyclic bases may also exist for other su(n), n>3.

hep-ph↗

arXiv2015

Linear Massive MIMO Precoders in the Presence of Phase Noise -- A Large-Scale Analysis

We study the impact of phase noise on the downlink performance of a multi-user multiple-input multiple-output system, where the base station (BS) employs a large number of transmit antennas $M$. We consider a setup where the BS employs $M_{\mathrm{osc}}$ free-running oscillators, and $M/M_{\mathrm{osc}}$ antennas are connected to each oscillator. For this configuration, we analyze the impact of phase noise on the performance of the regularized zero-forcing (RZF), when $M$ and the number of users $K$ are asymptotically large, while the ratio $M/K=β$ is fixed. We analytically show that the impact of phase noise on the signal-to-interference-plus-noise ratio (SINR) can be quantified as an effective reduction in the quality of the channel state information available at the BS when compared to a system without phase noise. As a consequence, we observe that as $M_{\mathrm{osc}}$ increases, the SINR performance of all considered precoders degrades. On the other hand, the variance of the random phase variations caused by the BS oscillators reduces with increasing $M_{\mathrm{osc}}$. Through Monte-Carlo simulations, we verify our analytical results, and compare the performance of the precoders for different phase noise and channel noise variances. For all considered precoders, we show that when $β$ is small, the performance of the setup where all BS antennas are connected to a single oscillator is superior to that of the setup where each BS antenna has its own oscillator. However, the opposite is true when $β$ is large and the signal-to-noise ratio at the users is low.

cs.IT↗

arXiv2014

Deviations from Tribimaximal Neutrino Mixing using a Model with $Δ(27)$ Symmetry

We present a model of neutrino mixing based on the flavour group $Δ(27)$ in order to account for the observation of a non-zero reactor mixing angle ($θ_{13}$). The model provides a common flavour structure for the charged-lepton and the neutrino sectors, giving their mass matrices a `circulant-plus-diagonal' form. Mass matrices of this form readily lead to mixing patterns with realistic deviations from tribimaximal mixing, including non-zero $θ_{13}$. With the parameters constrained by existing measurements, our model predicts an inverted neutrino mass hierarchy. We obtain two distinct sets of solutions in which the atmospheric mixing angle lies in the first and the second octants. The first (second) octant solution predicts the lightest neutrino mass, $m_3 \sim 29~\text{meV}$ ($m_3 \sim 65~\text{meV}$) and the $CP$ phase, $δ_{CP} \sim -\fracπ{4}$ ($δ_{CP} \sim \fracπ{2}$), offering the possibility of large observable $CP$ violating effects in future experiments.

hep-ph↗

arXiv2014

Fully Constrained Majorana Neutrino Mass Matrices using $Σ(72\times3)$

In 2002, two neutrino mixing ansatze having trimaximally mixed middle ($ν_2$) columns, namely tri-chi-maximal mixing ($\text{T}χ\text{M}$) and tri-phi-maximal mixing ($\text{T}ϕ\text{M}$), were proposed. It was recently shown that $\text{T}χ\text{M}$ with $χ=\pm \fracπ{16}$ as well as $\text{T}ϕ\text{M}$ with $ϕ= \pm \fracπ{16}$ leads to the solution, $\sin^2 θ_{13} = \frac{2}{3} \sin^2 \fracπ{16}$, consistent with the latest measurements of the reactor mixing angle, $θ_{13}$. To obtain $\text{T}χ\text{M}_{(χ=\pm \fracπ{16})}$ and $\text{T}ϕ\text{M}_{(ϕ=\pm \fracπ{16})}$, we utilised the type I see-saw framework with fully constrained Majorana neutrino mass matrices. These mass matrices also resulted in a relation among the neutrino masses, $m_1:m_2:m_3=\frac{\left(2+\sqrt{2}\right)}{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left(2+\sqrt{2}\right)}{-1+\sqrt{2(2+\sqrt{2})}}$. In this paper we construct a flavour model based on the discrete group $Σ(72\times3)$ and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric $3\times3$ matrix with 6 complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex 6 dimensional representation of $Σ(72\times3)$. Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.

hep-ph↗