Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

Department of Mathematics

This study investigates the risk from oil spills along the main shipping lane in the Red Sea based upon oil spill model trajectories forced by the outputs of validated high resolution regional met-ocean data. Following the intra-annual variations in the met-ocean conditions, the results are presented by classifying the basin into three regions: northern, central and southern Red Sea. The maximum distance traveled by the slick is presented for 1, 2, 5, 10, 14 and 20 days after the commencement of a spill. Different measures of hazard assessment in terms of the concentration of beached oil alongside the corresponding probability maps are also analyzed. The volume fractions of beached, dispersed and evaporated oil, 20 days after the commencement of a spill are quantified. The Red Sea general circulation is characterized by rich mesoscale eddies, which appear to be the most prevailing dynamics in oil transport in the basin. Two case events are analyzed to closely examine the effects of the mesoscale circulations on the fate of spilled oil. The results of this study provide a comprehensive assessment of oil spill hazards in the Red Sea, stemming its main shipping lane and identifies the areas at high risk that require timely mitigation strategies.

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Scientific Reports

Hazard assessment of oil spills along the main shipping lane in the Red Sea

We analyse the structure of finite dimensional subspaces of the set of points of strong subdifferentiability in a dual space. In a dual L1(μ) space, such a subspace is in the discrete part of the Yoshida-Hewitt type decomposition. In this set up, any Banach space consisting of points of strong subdifferentiability is necessarily finite dimensional. Our results also lead to streamlined and new proofs of results from the study of strong proximinality for subspaces of finite co-dimension in a Banach space. © 2021 Heldermann Verlag.

Journal of Convex Analysis

Structure of sets of strong subdifferentiability in dual L1-spaces

We define and discuss properties of the class of unbounded operators which attain minimum modulus. We establish a relationship between this class and the class of norm attaining bounded operators and compare the properties of both. Also we define absolutely minimum attaining operators (for not necessarily bounded) and characterize injective absolutely minimum attaining operators as those with compact generalized inverse. We give several consequences, one of those is that every such operator has a non trivial hyperinvariant subspace. © 2019, Forum D'Analystes, Chennai.

Journal of Analysis

Absolutely minimum attaining closed operators

The Minkowski function is a crucial tool used in the study of balanced domains and, more generally, quasi-balanced domains in several complex variables. If a quasi-balanced domain is bounded and pseudoconvex then it is well-known that its Minkowski function is plurisubharmonic. In this short note, we prove that under the additional assumption of smoothness of the boundary, the Minkowski function of a quasi-balanced domain is in fact smooth away from the origin. This allows us to construct a smooth plurisubharmonic defining function for such domains. Our result is new even in the case of balanced domains. © 2020 Informa UK Limited, trading as Taylor & Francis Group.

Complex Variables and Elliptic Equations

A note on the smoothness of the Minkowski function

arXiv preprint arXiv:2108.

Limits of an increasing sequence of complex manifolds

The paper deals with sampling and reconstruction of vector valued functions in a shift invariant space with multiple generators. Unlike the case of a shift invariant space with multiple generators in L2(R) , when the dimension of the vectors is the same as the number of generators, Z turns out to be a stable set of sampling. A sampling formula for reconstructing a function from its samples at integer points is derived and the problem of sampling on a perturbed set of integers is discussed. An illustration of sampling and reconstruction of a function in L2(R, R2) on a finite interval is given using Matlab. © 2020, Forum D'Analystes, Chennai.

Shift invariant spaces in L2(R, Cm) with m generators

In this paper we define and explore the analytic spread $\ell(\mathcal I)$ of a filtration in a local ring. We show that, especially for divisorial and symbolic filtrations, some basic properties of the analytic spread of an ideal extend to filtrations, even when the filtration is non Noetherian. We also illustrate some significant differences between the analytic spread of a filtration and the analytic spread of an ideal with examples. In the case of an ideal $I$, we have the classical bounds $\mbox{ht}(I)\le\ell(I)\le \dim R$. The upper bound $\ell(\mathcal I)\le \dim R$ is true for filtrations $\mathcal I$, but the lower bound is not true for all filtrations. We show that for the filtration $\mathcal I$ of symbolic powers of a height two prime ideal $\mathfrak p$ in a regular local ring of dimension three (a space curve singularity), so that $\mbox{ht}(\mathcal I) =2$ and $\dim R=3$, we have that $0\le \ell(\mathcal I)\le 2$ and all values of 0,1 and 2 can occur. In the cases of analytic spread 0 and 1 the symbolic algebra is necessarily non-Noetherian. The symbolic algebra is non-Noetherian if and only if $\ell(\mathfrak p^{(n)})=3$ for all symbolic powers of $\mathfrak p$ and if and only if $\ell(\mathcal I_a)=3$ for all truncations $\mathcal I_a$ of $\mathcal I$.

arXiv preprint arXiv:2104.

Analytic Spread of Filtrations and Symbolic Algebras

AGU Fall Meeting

Global Sensitivity Analysis of an Oil Spill Model: a Regularized Regression Approach

We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls the birth and death rate of the tumour cells. The cell volume fraction, cell velocity–fluid pressure system, and nutrient concentration are the model variables. A coupled system of a hyperbolic conservation law, a viscous fluid model, and a parabolic diffusion equation governs the dynamics of the model variables. The tumour boundary moves with the normal velocity of the outermost layer of cells, and this time-dependence is a challenge in designing and implementing a stable and fast numerical scheme. We recast the model into a form where the hyperbolic equation is defined on a fixed extended domain and retrieve the tumour boundary as the interface at which the cell volume fraction decreases below a threshold value. This procedure eliminates the need to track the tumour boundary explicitly and the computationally expensive re-meshing of the time-dependent domains. A numerical scheme based on finite volume methods for the hyperbolic conservation law, Lagrange P2- P1 Taylor-Hood finite element method for the viscous system, and mass-lumped finite element method for the parabolic equations is implemented in two spatial dimensions, and several cases are studied. We demonstrate the versatility of the numerical scheme in catering for irregular and asymmetric initial tumour geometries. When the nutrient diffusion equation is defined only in the tumour region, the model depicts growth in free suspension. On the contrary, when the nutrient diffusion equation is defined in a larger fixed domain, the model depicts tumour growth in a polymeric gel. We present numerical simulations for both cases and the results are consistent with theoretical and heuristic expectations such as early linear growth rate and preservation of radial symmetry when the boundary conditions are symmetric. The work presented here could be extended to include the effect of drug treatment of growing tumours. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Journal of Scientific Computing

Numerical Solution of a Two Dimensional Tumour Growth Model with Moving Boundary

In this study, a higher order compact (HOC) finite difference scheme is proposed for the simulation of multiphase flows with surface tension effects by coupling the pure streamfunction formulation of Navier–Stokes (N–S) equations with the level set method. Unlike most of the existing methods for multiphase flows that solve the incompressible Navier–Stokes equations in the velocity–pressure form or the stream-function vorticity form, we recast the governing equations into the biharmonic form of the N–S equations which carries stream-function $\psi$ as the only variable to be computed. The coupling of this formulation with level set (LS) enables the simulation of two phase flows by the core computation of only the single variable $\psi$ free from discontinuities in the whole physical domain. In the process, we also propose a novel hybrid HOC algorithm for post-processing the pressure on either side of the interface including the jump across it. The robustness of this method is established through a series of benchmark problems such as dispersion of capillary waves, static bubble and oscillating bubble at equilibrium in a fluid at rest and deforming circular drops in shear flows. We compare our numerical results with available benchmark results and excellent match is obtained in all the cases along with accurate representation of overall trends. Our approach is proved to be very efficient in terms of its easy implementation, relatively low computational time and high order of accuracy.