# Vasudevamurthy A STata Institute of Fundamental Research | TIFR · Faculty of Mathematics

Vasudevamurthy A S

PhD

## About

49

Publications

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337

Citations

## Publications

Publications (49)

We analyze a second order in space, first order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the bac...

In this study, we propose a machine learning technique for time-series data which combines statistical features and neural networks. The proposed algorithm is tested on various time series like stock prices, astronomical light curve and currency exchange rates. An implementation of reconstruction of unseen time series based on encodings learned by...

This article is a summary of major contributions of Indian mathematicians to the mathematical aspects of the finite element method in the last one decade: 2008–2017. We briefly trace out the historical origins of the topic in India and abroad. A section on the method itself is included so that this review is accessible to anybody with a background...

We present a nonlinear model for replacement, regulation of currency in circulation and hoarding currency. The nonlinearity enters the model in the regulatory term which depends on the total currency in the circulation. We provide an existence and uniqueness result for the model as well as its steady state. Local and global dynamics of the solution...

We analyze a second-order accurate finite difference method for a spatially periodic convection-diffusion problem. The method is a time stepping method based on the Strang splitting of the spatially semidiscrete solution, in which the diffusion part uses the Crank–Nicolson method and the convection part the explicit forward Euler approximation on a...

Higher order spectral element scheme is presented for Cahn–Hilliard equation in two and three dimensions. Legendre polynomial based nodal spectral element method is employed in space whereas explicit and semi-implicit schemes are discussed for time discretization.
Cahn–Hilliard equation conserves mass whereas it dissipates energy with time. These t...

In this paper higher order scheme is presented for two-dimensional sine-Gordon equation. Higher order Legendre spectral element method is used for space discretization which is basically a domain decomposition method and it retains all the advantages of spectral and finite element methods. Spectral stability analysis is performed for both homogeneo...

The nonlinear molecular deformation of the ferronematic liquid crystal in the presence of external applied magnetic field intensity is investigated in view of solitons for the director axis. The Frank’s free energy density of the nematic liquid crystal comprising the basic elastic deformations, molecular deformation associated with the nematic mole...

The sine–Gordonequation is a semilinear wave equation used to model many physical phenomenon like seismic events that includes earthquakes, slow slip and after-slip processes, dislocation in solids etc. Solution of homogeneous sine–Gordon equation exhibit soliton like structure that propagates without change in its shape and structure. The question...

A nonlinear nonlocal wave equation modelling the coupling between transverse and longitudinal vibrations was derived by Carrier in 1945. In 1968, using careful asymptotics, Narasimha derived a similar equation but with a different nonlinearity (nowadays referred as Kirchhoff type nonlinearity). In this study we solve both the equations numerically...

We consider optical flow estimation of flows with vorticity governed by 2D incompressible Euler and Navier-Stokes equations. A vorticity-streamfunction formulation and optimization techniques are used. We use Helmholtz decomposition of the velocity field and prove existence of an unique velocity and vorticity field for the linearized vorticity equa...

This is the second of a series of papers devoted to the study of h-p spectral element methods for three dimensional elliptic problems on non-smooth domains. The present paper addresses the proof of the main stability theorem. We assume that the differential operator is a strongly elliptic operator which satisfies Lax-Milgram conditions. The spectra...

A variational approach is used to recover fluid motion governed by Stokes and Navier-Stokes equations. Unlike previous approaches where optical flow method is used to track rigid body motion, this new framework aims at investigating incompressible flows using optical flow techniques. We formulate a minimization problem and determine conditions unde...

An inviscid model for the sea breeze derived from the viscous model of Li and Smith (J Atmos Sci 67:2752–2765, 2010) [thereafter used by Jiang (J Atmos Sci 69:1890–1909, 2012)] has been considered. The apparent singularities appearing in the inviscid case has been analyzed rigorously and shown that they can be removed easily by taking limits of the...

This is the first of a series of papers devoted to the study of h-p spectral element methods for solving three dimensional elliptic boundary value problems on non-smooth domains using parallel computers. In three dimensions there are three different types of singularities namely; the vertex, the edge and the vertex-edge singularities. In addition t...

A variational approach is used to recover fluid motion governed by
Stokes and Navier-Stokes equations. Unlike previous approaches where optical
flow method is used to track rigid body motion, this new framework aims at
investigating incompressible flows using optical flow techniques. We formulate
a minimization problem and determine conditions unde...

We consider the numerical solution by finite difference methods of the heat equation in one space dimension, with a nonlocal integral boundary condition, resulting from the truncation to a finite interval of the problem on a semi-infinite interval. We first analyze the forward Euler method, and then the theta-method for 0 < theta <= 1, in both case...

We present an efficient and novel numerical algorithm for inversion of transforms arising in imaging modalities such as ultrasound imaging, thermoacoustic and photoacoustic tomography, intravascular imaging, non-destructive testing, and radar imaging with circular acquisition geometry. Our algorithm is based on recently discovered explicit inversio...

We give a general class of functionals for which the phase space Feynman path integrals of higher order parabolic type have a mathematically rigorous meaning. More precisely, for any functional belonging to our class, the time slicing approximation of the phase space path integral converges uniformly on compact subsets with respect to the endpoint...

We propose an optical flow algorithm based on variational methods to recover fluid motion governed by Stokes and Navier-Stokes equations. Unlike previous approaches where optical flow method is used to track rigid body motion, this new framework aims to recover underlying fluid motion by tracing passive scalars using flow dynamics constraints. We f...

We consider optical flow estimation of flows with vorticity governed by 2D incompressible Euler and Navier–Stokes equations
. A vorticity-streamfunction formulation and optimization techniques are used. We use Helmholtz decomposition of the velocity field and prove existence of an unique velocity and vorticity field for the linearized vorticity equ...

We present an efficient and novel numerical algorithm for inver-sion of transforms arising in imaging modalities such as ultrasound imaging, thermoacoustic and photoacoustic tomography, intravascular imaging, non-destructive testing, and radar imaging with circular acquisition geometry. Our algorithm is based on recently discovered explicit inversi...

This paper is devoted to the study of non-conforming h-ph-p spectral element methods for three dimensional elliptic problems on non-smooth domains using parallel computers. To overcome the singularities which arise in the neighbourhoods of vertices, edges and vertex-edges we use local systems of coordinates together with geometric meshes which beco...

A new linear model for the sea breeze circulation that includes Coriolis effect, crucial for the tropical region, and a non-zero background wind speed is derived from the mesoscale equations. Earlier studies of Rotunno (J Atmos Sci 40(8):1999–2009, 1983) and Qian et al. (J Atmos Sci 66(6):1749, 2009) considered these effects separately. These two m...

In 1968 Roddam Narasimha (RN) published a paper in Journal of Sound and Vibration (JSV) deriving the equation
$$\frac{{{\partial ^2}v}}
{{\partial {t^2}}} + 2R\frac{{\partial v}}
{{\partial t}} = \left[ {1 + \frac{1}
{2}\Gamma '\int\limits_0^l {v_x^2dx} } \right]\frac{{{\partial ^2}v}}
{{\partial {t^2}}} + {f_0}\left( {x,t} \right)$$ (1.1) for the...

Considering the linearized boundary layer equations for three-dimensional disturbances, a Mangler type transformation is used to reduce this case to an equivalent two-dimensional one.

A variable resolution global spectral method is created on the sphere using High resolution Tropical Belt Transformation (HTBT). HTBT belongs to a class of map called reparametrisation maps. HTBT parametrisation of the sphere generates a clustering of points in the entire tropical belt; the density of the grid point distribution decreases smoothly...

For weakly hyperbolic heat equation a numerical scheme based on multiple scale technique is derived. The advantages over the conventional finite difference method are highlighted.

In this paper we introduce a slight modification to the relaxation system of Jin and Xin which approximates a conservation law. The proposed alternate system satisfies an integral constraint that is more consistent than the standard one while retaining the semilinear structure. We establish L∞ estimates under the usual subcharacteristic condition a...

The slow-manifold for the Lorenz-Krishnamurthy model has been studied. By minimizing the evolution rate we ¯nd that the analytical functions for the fast variables are devoid of high frequency oscillations. However upon solving this model with initial values of the fast variables obtained from the analytical functions, the LK model exhibits high fr...

This paper presents a complete asymptotic analysis of a simple model for the evolution of the nocturnal temperature distribution on bare soil in calm clear conditions. The model is based on a simplified flux emissivity scheme that provides a nondiffusive local approximation for estimating longwave radiative cooling near ground. An examination of th...

As radiation plays a key role in the determination of the near-surface thermal environment, great accuracy is required in the computation of radiative fluxes, especially because a small error in the fluxes can lead to large errors in estimated cooling rates. A new code that employs a novel numerical scheme for making precise estimates of longwave f...

A series of numerical simulations using a one-dimensional energy balance model suggest that both the depth and the intensity of the nocturnal temperature inversion depend on surface emissivity εg and a ground cooling rate parameter β (which in the model is a surrogate for the inverse square root of the soil thermal diffusivity), especially under ca...

In this paper we study a system of nonlinear partial differential equations which we write as a Burgers equation for matrix
and use the Hopf-Cole transformation to linearize it. Using this method we solve initial value problem and initial boundary
value problems for some systems of parabolic partial differential equations. Also we study an initial...

This paper concerns a phenomenon called the Ramdas Paradox by Lettau, referring to the occurrence of a minimum in the temperature some decimetres above ground on calm clear nights. Recently, Vasudeva Murthy, Srinivasan and Narasimha have proposed a theory that successfully reproduces the observed minima. We extend that work here to investigate the...

In this paper the authors analyze splitting errors in numerical schemes for a semilinear system of ordinary differential equations (ODEs). It is well known that errors occur even when splitting the continuous fully linear system analytically, consequently splitting numerical schemes introduces additional errors. A general approach to delineate and...

Summary: We propose a one-dimensional model for the vorticity equation involving viscosity. Complex methods are utilized in order to study finite time blow-up of the solutions. In particular, it is shown that the blow-up time depends monotoneously on the viscosity.

This paper is concerned with the numerical solution of the Cauchy problem for the Benjamin-Ono equationu
t
+uu
x
−Hu
xx
=0, whereH denotes the Hilbert transform. Our numerical method first approximates this Cauchy problem by an initial-value problem for a corresponding 2L-periodic problem in the spatial variable, withL large. This periodic problem...

We propose a new viscous term in the Constantin-Lax-Majda 1D model for the 3D vorticity equation. This overcomes the drawback associated with the canonical viscous term considered by Schochet.

In a recent paper by Hohlfeld et al., the authors introduced a method called `differential inversion' (DI) for solving Fredholm integral equations of the first kind in convolution form. In this method the solution was expressed in a series involving successive derivatives of the known function. The coefficients in this expansion were computed from...

On calm clear nights, air at a height of a few decimetres above bare soil can be cooler than the surface by several degrees in what we shall call the Ramdas layer (Ramdas and Atmanathan, 1932). The authors have recently offered a logical explanation for such a lifted temperature minimum, together with a detailed numerical model. In this paper, we p...

Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u t =–A2 u. Using a representation of the semi group exp(–A2 t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w t = w yy , with initial values v solving the initial value problem for v y = iAv. Thi...

Numerous reports from several parts of the world have confirmed that on calm clear nights a minimum in air temperature can occur just above ground, at heights of the order of 1/2 m or less. This phenomenon, first observed by Ramdas & Atmanathan (1932), carries the associated paradox of an apparently unstable layer that sustains itself for several h...

The subject of this note is the numerical integration in time of nonclassical parabolic initial-boundary value problems which involve nonlocal integral terms over the spatial domain. The integral terms may appear in the boundary conditions and/or in the governing partial differential equation itself. These terms generally complicate the application...

The object of this paper is to study some boundary element methods for the heat equation. Two approaches are considered. The first, based on the heat potential, has been studied numerically by previous authors. Here the convergence analysis in one space dimension is presented. In the second approach, the heat equation is first descretized in time a...

The knowledge of inversion height in the nocturnal boundary layer (NBL) under calm clear conditions is crucial in deter-mining the fate of chemical pollutants that are (accidentally or otherwise) released into the atmosphere. A new analytical expression for temperature profiles over bare soil surfaces under calm clear conditions is used to study in...