arXiv subjects

Amey Joshi

Publications and source records attributed to Amey Joshi.

5 recordsLinked to original sources

arXiv2026

Spectral Sequences in Lasagna Theory

We use Khovanov-Floer theories and their spectral sequences to construct differentials on the corresponding skein-lasagna modules. Then we show that for 2-handlebodies, a spectral sequence of TQFTs coming from a Khovanov-Floer theory gives a spectral sequence of lasagna modules under the aforementioned differential. As a corollary, we recover the rank inequality between the Khovanov and Lee lasagna modules. We also prove certain properties like the connect-sum formula that these spectral sequences satisfy.

math.GT↗

arXiv2018

Can Sound Waves be Slowed?

Dielectric fluids experience a striction force in the presence of an external electric field. Although the striction force on the entire body of the fluid is usually zero, it does contribute to its deformations. In this paper, I show that the speed of sound in dielectric fluids is reduced when they are exposed to uniform electric fields of sufficiently high magnitude. Ferrofluids also experience a similar striction force in presence of a magnetizing field. However, their low relative permeability makes the effect very small.

physics.flu-dyn↗

arXiv2016

Plane Poiseuille flow through a porous medium - an analytical solution

This paper develops a closed-form, analytical expression for the Darcy velocity of a Newtonian fluid flowing through a channel filled with a porous medium, bound by rigid walls and driven by a constant pressure gradient. We express the Darcy velocity as a Weierstrass elliptic function of the transverse coordinate. It allows us to get analytical expressions for volume flux and the rate of dissipation. The Weierstrass elliptic function is a doubly-periodic, complex-valued function defined over the complex plane. It takes real values only on certain segments in the complex plane. We show how to align the transverse coordinate axis along these segments to ensure real values of Darcy velocity. Lastly, we give an algorithm to generate velocity profile and compute volume flux given the flow parameters.

physics.flu-dyn↗

arXiv2013

Rayleigh-Taylor Instability in Viscoelastic Fluids

In this paper I analyze the onset of Rayleigh-Taylor instability between two linear viscoelastic fluids assuming that the perturbations at the interface are small. In the first half, the paper analyzes a stratified viscoelastic fluid in which I prove that the perturbations rise or fall exponentially without oscillating. The second half of the paper examines the effect of electric and magnetic fields on viscoelastic fluids. I show that it is possible to choose electric or magnetic field gradient such that the effective acceleration due to gravity is zero. If a heavy Newtonian fluid rests on top of a lighter Newtonian fluid such a choice of field gradient would have rendered the arrangement stable. If the fluids are viscoelastic, I show that a similar arrangement is unstable.

physics.flu-dyn↗

arXiv2013

Stress due to Electric and Magnetic fields in Viscoelastic Fluids

A clear understanding of body force densities due to external electromagnetic fields is necessary to study flow and deformation of materials exposed to the fields. In this paper, we derive an expression for stress in continua with viscous and elastic properties in presence of external, static electric or magnetic fluids. Our derivation follows from fundamental thermodynamic principles. We demonstrate the soundness of our results by showing that they reduce to known expressions for Newtonian fluids and elastic solids. We point out the extra care to be taken while applying these techniques to permanently polarized or magnetized materials and derive an expression for stress in a ferro-fluid. Lastly, we derive expressions for ponderomotive forces in several situations of interest to fluid dynamics and rheology.

physics.flu-dyn↗