Arun Verma | Hampton University (original) (raw)

Papers by Arun Verma

Research paper thumbnail of Existence of torsional surface wave in a porous crustal layer over an initially stressed inhomogeneous half-space

Journal of Vibration and Control

ABSTRACT In this short communication, a mathematical model for torsional wave propagation in a po... more ABSTRACT In this short communication, a mathematical model for torsional wave propagation in a porous crustal layer lying over an anisotropic inhomogeneous half-space has been studied. This study reveals that the inhomogeneity in the half-space is assumed to be present in the directional rigidities and density. The anisotropy nature of the half-space is due to the presence of initial stress. Bessels functions are taken to solve the problem and the frequency equations governing the propagation of torsional waves are derived. It has been observed that there are three sets of torsional wave fronts and one shear wave front. Each set of torsional wave front has a pronounced effect on phase velocity, whereas shear wave front remains un-affected. Numerical treatment is applied to seek these effects on phase velocity of the existing waves and presented graphically. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed.

Research paper thumbnail of Simple Map with Low MN Perturbation for a Single-Null Divertor Tokamak with Constant Width of Stochastic Layer

In this work, we investigate the effects of low MN perturbations in a single-null divertor tokama... more In this work, we investigate the effects of low MN perturbations in a single-null divertor tokamak with stochastic scrape-off layer. The unperturbed magnetic topology of a single-null divertor tokamak is represented by Simple Map (Punjabi A, Verma A and Boozer A, Phys Rev Lett), 69, 3322 (1992) and J Plasma Phys, 52, 91 (1994). We choose the combinations of the

Research paper thumbnail of Ekman-flow induced by a naturally permeable bed

Research paper thumbnail of Existence of torsional surface wave in a porous crustal layer over an initially stressed inhomogeneous half-space

Journal of Vibration and Control

In this short communication, a mathematical model for torsional wave propagation in a porous crus... more In this short communication, a mathematical model for torsional wave propagation in a porous crustal layer lying over an anisotropic inhomogeneous half-space has been studied. This study reveals that the inhomogeneity in the half-space is assumed to be present in the directional rigidities and density. The anisotropy nature of the half-space is due to the presence of initial stress. Bessels functions are taken to solve the problem and the frequency equations governing the propagation of torsional waves are derived. It has been observed that there are three sets of torsional wave fronts and one shear wave front. Each set of torsional wave front has a pronounced effect on phase velocity, whereas shear wave front remains un-affected. Numerical treatment is applied to seek these effects on phase velocity of the existing waves and presented graphically. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed.

Research paper thumbnail of Area of Stochastic Scrape-Off Layer for a Single-Null Divertor Tokamak Using Simple Map

The magnetic topology of a single-null divertor tokamak is represented by Simple Map (Punjabi A, ... more The magnetic topology of a single-null divertor tokamak is represented by Simple Map (Punjabi A, Verma A and Boozer A, Phys Rev Lett), 69, 3322 (1992) and J Plasma Phys, 52, 91 (1994). The Simple map is characterized by a single parameter k representing the toroidal asymmetry. The width of the stochastic scrape-off layer and its area varies with the

Research paper thumbnail of Symmetric Simple Map with Low MN Perturbations for Single Null Divertor Tokamak

Research paper thumbnail of Fluctuating Flow Induced by a Rotating Disc

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1983

Fluid motion induced by the rotational vibrations of an infinite disc rotating with angular veloc... more Fluid motion induced by the rotational vibrations of an infinite disc rotating with angular velocity Ω ( a + b cos ωT ) in contact with an incompressible viscous fluid of semi-infinite extent is analysed when the ampli­tude parameter α ( = b/a ) varies from zero to infinity. Composite solutions valid over the whole of the flow régime and specific expressions for the shearing stress components at the disc and for the axial flow in the far region are obtained for low and high frequencies of periodic fluctuations. An attempt is made to calculate the frequency of overlap of the two solutions. Using the method of matched asymptotic expansions, we find that the thickness of the region of mean flow increases with α . New esti­mates of the thickness of the outer region are obtained for the fluid motion induced by torsional oscillations of a plane lamina.

Research paper thumbnail of Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface

Journal of Vibration and Control, 2014

In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal laye... more In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.

Research paper thumbnail of The simple map for a single-null divertor tokamak

Journal of Plasma Physics, 1996

We present the simple map for a single-null divertor tokamak. The simple map is an area-preservin... more We present the simple map for a single-null divertor tokamak. The simple map is an area-preserving map based on the idea that magnetic field lines are a single-degree- of-freedom time-dependent Hamiltonian system, and that the basic features of such systems near the X-point are generic. We obtain the properties of this map and the resulting footprints of field lines on the divertor plate. These include the width of the stochastic layer, the edge safety factor, the area of the footprint and the amount of magnetic flux diverted. We give the safety factor profile, the average and median values of strike angles, lengths and the Liapunov exponents. We describe how the effects of magnetic perturbations can be included in the simple map. We show how the map can be applied to the problem of the determination of heat flux on the divertor plate in tokamaks.

Research paper thumbnail of A note on oscillatory horizontal layer over a permeable BED

International Journal of Engineering Science, 1983

Abstract The time dependent fluid motion, induced by a harmonic oscillation of a very porous matr... more Abstract The time dependent fluid motion, induced by a harmonic oscillation of a very porous matrix imbeded in a liquid layer of finite depth is studied. Generalized Darcy law is employed to analyse the fluid motion within the permeable bed.

Research paper thumbnail of Rotationally symmetric fluctuating flow about a rotating disk

International Journal of Engineering Science, 1984

Research paper thumbnail of The simple map for a single-null divertor tokamak

Journal of plasma physics, 1996

We present the simple map for a single-null divertor tokamak. The simple map is an area-preservin... more We present the simple map for a single-null divertor tokamak. The simple map is an area-preserving map based on the idea that magnetic field lines are a single-degree-of-freedom time-dependent Hamiltonian system, and that the basic features of such systems near the X-point are ...

Research paper thumbnail of Tokamak divertor maps

Journal of plasma physics, 1994

A mapping method is developed to investigate the problem of determination and control of heat-dep... more A mapping method is developed to investigate the problem of determination and control of heat-deposition patterns on the plates of a tokamak divertor. The deposition pattern is largely determined by the magnetic field lines, which are mathematically equivalent to the trajectories of a single-degree-of-freedom time-dependent Hamiltonian system. Maps are natural tools to study the generic features of such systems. The general theory of maps is presented, and methods for incorporating various features of the magnetic field and particle motion in divertor tokamaks are given. Features of the magnetic field include the profile of the rotational transform, single- versus double-null divertor, reverse map, the effects of naturally occurring low M and N, and externally imposed high-M, high-N perturbations. Particle motion includes radial diffusion, pitch angle and energy scattering, and the electric sheath at the plate. The method is illustrated by calculating the stochastic broadening in a single- null divertor tokamak. Maps provide an efficient, economic and elegant method to study the problem of motion of plasma particles in the stochastic scrape-off layer.

Research paper thumbnail of Stochastic broadening of the separatrix of a tokamak divertor

Physical Review Letters, 1992

The plasma in a modern tokamak is bounded by a separatrix between magnetic field lines that form ... more The plasma in a modern tokamak is bounded by a separatrix between magnetic field lines that form toroidal magnetic surfaces, on which the plasma is confined, and open field lines that divert the plasma exhaust to so-called divertor plates. This separatrix is sharp in an ...

Research paper thumbnail of Existence of torsional surface wave in a porous crustal layer over an initially stressed inhomogeneous half-space

Journal of Vibration and Control

ABSTRACT In this short communication, a mathematical model for torsional wave propagation in a po... more ABSTRACT In this short communication, a mathematical model for torsional wave propagation in a porous crustal layer lying over an anisotropic inhomogeneous half-space has been studied. This study reveals that the inhomogeneity in the half-space is assumed to be present in the directional rigidities and density. The anisotropy nature of the half-space is due to the presence of initial stress. Bessels functions are taken to solve the problem and the frequency equations governing the propagation of torsional waves are derived. It has been observed that there are three sets of torsional wave fronts and one shear wave front. Each set of torsional wave front has a pronounced effect on phase velocity, whereas shear wave front remains un-affected. Numerical treatment is applied to seek these effects on phase velocity of the existing waves and presented graphically. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed.

Research paper thumbnail of Simple Map with Low MN Perturbation for a Single-Null Divertor Tokamak with Constant Width of Stochastic Layer

In this work, we investigate the effects of low MN perturbations in a single-null divertor tokama... more In this work, we investigate the effects of low MN perturbations in a single-null divertor tokamak with stochastic scrape-off layer. The unperturbed magnetic topology of a single-null divertor tokamak is represented by Simple Map (Punjabi A, Verma A and Boozer A, Phys Rev Lett), 69, 3322 (1992) and J Plasma Phys, 52, 91 (1994). We choose the combinations of the

Research paper thumbnail of Ekman-flow induced by a naturally permeable bed

Research paper thumbnail of Existence of torsional surface wave in a porous crustal layer over an initially stressed inhomogeneous half-space

Journal of Vibration and Control

In this short communication, a mathematical model for torsional wave propagation in a porous crus... more In this short communication, a mathematical model for torsional wave propagation in a porous crustal layer lying over an anisotropic inhomogeneous half-space has been studied. This study reveals that the inhomogeneity in the half-space is assumed to be present in the directional rigidities and density. The anisotropy nature of the half-space is due to the presence of initial stress. Bessels functions are taken to solve the problem and the frequency equations governing the propagation of torsional waves are derived. It has been observed that there are three sets of torsional wave fronts and one shear wave front. Each set of torsional wave front has a pronounced effect on phase velocity, whereas shear wave front remains un-affected. Numerical treatment is applied to seek these effects on phase velocity of the existing waves and presented graphically. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed.

Research paper thumbnail of Area of Stochastic Scrape-Off Layer for a Single-Null Divertor Tokamak Using Simple Map

The magnetic topology of a single-null divertor tokamak is represented by Simple Map (Punjabi A, ... more The magnetic topology of a single-null divertor tokamak is represented by Simple Map (Punjabi A, Verma A and Boozer A, Phys Rev Lett), 69, 3322 (1992) and J Plasma Phys, 52, 91 (1994). The Simple map is characterized by a single parameter k representing the toroidal asymmetry. The width of the stochastic scrape-off layer and its area varies with the

Research paper thumbnail of Symmetric Simple Map with Low MN Perturbations for Single Null Divertor Tokamak

Research paper thumbnail of Fluctuating Flow Induced by a Rotating Disc

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1983

Fluid motion induced by the rotational vibrations of an infinite disc rotating with angular veloc... more Fluid motion induced by the rotational vibrations of an infinite disc rotating with angular velocity Ω ( a + b cos ωT ) in contact with an incompressible viscous fluid of semi-infinite extent is analysed when the ampli­tude parameter α ( = b/a ) varies from zero to infinity. Composite solutions valid over the whole of the flow régime and specific expressions for the shearing stress components at the disc and for the axial flow in the far region are obtained for low and high frequencies of periodic fluctuations. An attempt is made to calculate the frequency of overlap of the two solutions. Using the method of matched asymptotic expansions, we find that the thickness of the region of mean flow increases with α . New esti­mates of the thickness of the outer region are obtained for the fluid motion induced by torsional oscillations of a plane lamina.

Research paper thumbnail of Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface

Journal of Vibration and Control, 2014

In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal laye... more In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.

Research paper thumbnail of The simple map for a single-null divertor tokamak

Journal of Plasma Physics, 1996

We present the simple map for a single-null divertor tokamak. The simple map is an area-preservin... more We present the simple map for a single-null divertor tokamak. The simple map is an area-preserving map based on the idea that magnetic field lines are a single-degree- of-freedom time-dependent Hamiltonian system, and that the basic features of such systems near the X-point are generic. We obtain the properties of this map and the resulting footprints of field lines on the divertor plate. These include the width of the stochastic layer, the edge safety factor, the area of the footprint and the amount of magnetic flux diverted. We give the safety factor profile, the average and median values of strike angles, lengths and the Liapunov exponents. We describe how the effects of magnetic perturbations can be included in the simple map. We show how the map can be applied to the problem of the determination of heat flux on the divertor plate in tokamaks.

Research paper thumbnail of A note on oscillatory horizontal layer over a permeable BED

International Journal of Engineering Science, 1983

Abstract The time dependent fluid motion, induced by a harmonic oscillation of a very porous matr... more Abstract The time dependent fluid motion, induced by a harmonic oscillation of a very porous matrix imbeded in a liquid layer of finite depth is studied. Generalized Darcy law is employed to analyse the fluid motion within the permeable bed.

Research paper thumbnail of Rotationally symmetric fluctuating flow about a rotating disk

International Journal of Engineering Science, 1984

Research paper thumbnail of The simple map for a single-null divertor tokamak

Journal of plasma physics, 1996

We present the simple map for a single-null divertor tokamak. The simple map is an area-preservin... more We present the simple map for a single-null divertor tokamak. The simple map is an area-preserving map based on the idea that magnetic field lines are a single-degree-of-freedom time-dependent Hamiltonian system, and that the basic features of such systems near the X-point are ...

Research paper thumbnail of Tokamak divertor maps

Journal of plasma physics, 1994

A mapping method is developed to investigate the problem of determination and control of heat-dep... more A mapping method is developed to investigate the problem of determination and control of heat-deposition patterns on the plates of a tokamak divertor. The deposition pattern is largely determined by the magnetic field lines, which are mathematically equivalent to the trajectories of a single-degree-of-freedom time-dependent Hamiltonian system. Maps are natural tools to study the generic features of such systems. The general theory of maps is presented, and methods for incorporating various features of the magnetic field and particle motion in divertor tokamaks are given. Features of the magnetic field include the profile of the rotational transform, single- versus double-null divertor, reverse map, the effects of naturally occurring low M and N, and externally imposed high-M, high-N perturbations. Particle motion includes radial diffusion, pitch angle and energy scattering, and the electric sheath at the plate. The method is illustrated by calculating the stochastic broadening in a single- null divertor tokamak. Maps provide an efficient, economic and elegant method to study the problem of motion of plasma particles in the stochastic scrape-off layer.

Research paper thumbnail of Stochastic broadening of the separatrix of a tokamak divertor

Physical Review Letters, 1992

The plasma in a modern tokamak is bounded by a separatrix between magnetic field lines that form ... more The plasma in a modern tokamak is bounded by a separatrix between magnetic field lines that form toroidal magnetic surfaces, on which the plasma is confined, and open field lines that divert the plasma exhaust to so-called divertor plates. This separatrix is sharp in an ...