Searcharxiv⌕ Search

arXiv subjects

R. V. R. Pandya

Publications and source records attributed to R. V. R. Pandya.

17 recordsLinked to original sources
arXiv2022

Generalized Attention Mechanism and Relative Position for Transformer

In this paper, we propose generalized attention mechanism (GAM) by first suggesting a new interpretation for self-attention mechanism of Vaswani et al. . Following the interpretation, we provide description for different variants of attention mechanism which together form GAM. Further, we propose a new relative position representation within the framework of GAM. This representation can be easily utilized for cases in which elements next to each other in input sequence can be at random locations in actual dataset/corpus.

cs.CL↗
arXiv2015

Comments on turbulence theory by Qian and by Edwards and McComb

We reexamine Liouville equation based turbulence theories proposed by Qian {[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys. A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov spectrum. These theories obtained identical equation for spectral density $q(k)$ and different results for damping coefficient. Qian proposed variational approach and Edwards and McComb proposed maximal entropy principle to obtain equation for the damping coefficient. We show that assumptions used in these theories to obtain damping coefficient correspond to unphysical conditions.

physics.flu-dyn↗
arXiv2015

Dispersed Phase of Non-Isothermal Particles in Rotating Turbulent Flows

We suggest certain effects, caused by interaction between rotation and gravitation with turbulence structure, for the cooling/heating of dispersed phase of non-isothermal particles in rotating turbulent fluid flows. These effects are obtained through the derivation of kinetic or probability density function based macroscopic equations for the particles. In doing so, for one-way temperature coupling, we also show that homogeneous, isotropic non-isothermal fluid turbulence does not influence the mean temperature (though it influences mean velocity) of the dispersed phase of particles settling due to gravitational force in the isotropic turbulence.

physics.flu-dyn↗
arXiv2015

Jets with Reversing Buoyancy

A jet of heavy fluid is injected upwards, at time $t=0$, into a lighter fluid and reaches a maximum height at time $t=t_i$ and then flows back around the upward flow. A similar flow situation occurs for a light fluid injected downward into a heavy one. In this paper an exact analytical expression for $t_i$ is derived. The expression remains valid for laminar and turbulent buoyant jets with or without swirl.

physics.flu-dyn↗
arXiv2014

Development of Eulerian Theory of Turbulence within Kraichnan's Direct Interaction Approximation Framework

Within the framework of Kraichnan's Direct Interaction Approximation (DIA), we propose an Eulerian turbulence theory providing a closed set of equations for two-time and single-time velocity correlations, and second order correlations of infinitesimal response tensor $\hat{G}_{in}({\bf k};t,t')$. The proposed theory, namely variant of DIA (VDIA), is consistent with Kolmogorov's energy spectrum. The VDIA is further modified to make it compatible with random Galilean transformation rules. The closed set of equations does not contain equation for ensemble averaged response tensor $G_{in}({\bf k};t,t')=\langle\hat{G}_{in}({\bf k};t,t')\rangle$. The present theory can also be seen as a new remormalized perturbation theory having different method for renormalization.

physics.flu-dyn↗
arXiv2013

A new Eulerian theory of turbulence constrained by random Galilean invariance

We propose a new Eulerian turbulence theory to obtain a closed set of equations for homogeneous, isotropic turbulent velocity field correlations and propagator functions by incorporating constraints of random Galilean invariance. This incorporation generates a few different equations for propagator and the present theory suggests a way to utilize them into the closure solutions of two-time and single-time velocity correlations' equations so as to properly account for random sweeping phenomena. The present theory yields exact solutions when applied to simple model problem of random oscillator.

math-ph↗
arXiv2012

Modification in Silling's Peridynamic Formulation of Elasticity Theory for Discontinuities and Long-Range Forces

We suggest modified version of Silling's peridynamic equation of motion within the framework of Silling's peridynamics formulation (J. Mech. Phys. Solids {\bf 48}, pp.175-209, 2000) of elasticity theory. The modified equation contains an additional damping force term. This term can eliminate artificial oscillations in displacement field at large values of time as predicted by Silling's peridynamic equation.

math-ph↗
arXiv2007

Clarifying Einstein's First Derivation for Mass-Energy Equivalence and Consequently Making Ives's Criticism a Void

We study physical situation considered by Einstein (Ann. Physik, 17, 1905) for his first derivation of mass-energy equivalence. Einstein introduced a constant $C$ in his derivation and reasoning surrounding $C$ and equations containing $C$ caused criticism by Ives. Here we clarify Einstein's derivation and obtain a value for constant $C$. The obtained zero value for $C$ suggests alternative explanation for Einstein's derivation and makes Ives's criticism a void and for which details are also presented in this paper.

physics.hist-ph↗
arXiv2006

Size of Memory Objects

I consider model for flares proposed by P.-G de Gennes (PNAS, 101 (44), 15778-15781, 2004) and suggest a range for amplification factor (I) for inhibitory neurons for the time evolution of non-divergent generations of excitatory neurons which eventually die out. The exact numerical solution of the model for the suggested range of the factor (I) then provides minimum number of neurons describing size (M) for memory objects. The obtained size is M = 8 to 12.75 and which is larger than the size M = 2 to 4 as obtained theoretically by de Gennes.

physics.bio-ph↗
arXiv2006

Scaling of Circulation in Buoyancy Generated Vortices

The temporal evolution of the fluid circulation generated by a buoyancy force when two-dimensional (2D) arrays of 2D thermals are released into a quiescent incompressible fluid is studied through the results of numerous lattice Boltzmann simulations. It is observed that the circulation magnitude grows to a maximum value in a finite time. When both the maximum circulation and the time at which it occurs are non-dimensionalised by appropriately defined characteristic scales, it is shown that two simple Prandtl number (Pr) dependent scaling relations can be devised that fit these data very well over nine decades of Pr spanning the viscous and diffusive regimes and six decades of Rayleigh number (Ra) in the low Ra regime. Also, obtained analytically is the exact result that circulation magnitude continues to grow in time for a single buoyant vortex ring in an infinite unbounded fluid.

physics.flu-dyn↗
arXiv2006

Scaling of Spinodal Turbulence between Viscous and Inertial Hydrodynamic Regimes

The existence of unique scaling in a crossover regime between viscous and inertial hydrodynamic regimes is revealed for homogeneous, isotropic, incompressible, spinodal turbulence which is characterized, to begin with, by three different length scales and a velocity scale. The obtained scaling exponents are found to be in agreement and in consistency with available simulation results for a broad range of crossover regime. Also, it is observed that the spinodal turbulence in the crossover regime is in complete consistency with the universality class of self-preservation of decaying grid turbulence. We then obtain analytical forms for various scalings, valid in the crossover regime, through the analysis for self-preservation of spinodal turbulence.

cond-mat.soft↗
arXiv2006

Increased Crowding during Escape Panic and Suitable Strategy for its Avoidance

Under panicky situation, human have tendency to rush toward a particular direction for escape. I show here that this tendency alone causes increase in crowding and which could eventually trigger jamming that is not preferable. Further, it is proposed that potential flow theory can be employed in finding suitable strategy for escape.

physics.soc-ph↗
arXiv2005

Generalized model for human dynamics

Human dynamics model consistent with our natural ability to perform different activities is put forward by first arguing limitations of the model suggested by Barabasi (Nature, 435, 207-211, 2005).

physics.soc-ph↗
arXiv2005

Influence of Gravitation on Mass-Energy Equivalence Relation

We study influence of gravitational field on the mass-energy equivalence relation by incorporating gravitation in the physical situation considered by Einstein (Ann. Physik, 17, 1905, English translation in ref. [1]) for his first derivation of mass-energy equivalence. In doing so, we also refine Einstein's expression (Ann. Physik, 35, 1911, English translation in ref. [3]) for increase in gravitational mass of the body when it absorbs E amount of radiation energy.

physics.gen-ph↗
arXiv2004

Model representation for local energy transfer theory of isotropic turbulence

An almost-Markovian model equation is proposed for Fourier modes of velocity field of isotropic turbulence whose statistical properties are identical to those governed by equations of Local Energy Transfer theory of turbulence [McComb et al., J. Fluid Mech. {\bf 245}, 279 (1992)] compatible with the Kolmogorov spectrum.

cond-mat.stat-mech↗