arXiv subjects

Kiran M. Kolwankar

Publications and source records attributed to Kiran M. Kolwankar.

At least 19 recordsLinked to original sources

arXiv2025

Symmetric Lévy flights in semi-infinite domain

We study symmetric Lévy flights in a semi-infinite domain $[0,\infty)$ with a reflecting and absorbing boundary at 0. To this end, we use the fractional differential equation that governs the Lévy process. Incorporating the boundary conditions in Lévy flights has been an open and tricky question, as the long jumps can lead to the Lévy flights leaping over the boundary. We, for the first time, incorporate reflecting and absorbing boundary conditions for Lévy flights and solve the fractional differential equation analytically to find the probability densities. Monte Carlo simulations are also performed for both boundary conditions to verify the results. Analytical and simulation results perfectly coincide for the reflecting boundary condition and, for the absorbing boundary condition, they coincide for the large abscissa values.

cond-mat.stat-mech↗

arXiv2021

Low-cost experiment to measure the speed of light

In this paper, we demonstrate a low-cost method to measure the speed of light. It uses instruments which are readily available in any undergraduate laboratory in a developing country and some components which are inexpensive. The method is direct as it measures the time of flight of the LASER beam and easy to implement. It will allow students to verify the finite value of the speed of light first hand. It can be part of the undergraduate syllabus as a regular experiment or a demonstration experiment.

physics.ed-ph↗

arXiv2019

Chaotic Properties of Single Element Nonlinear Chimney Model: Effect of Directionality

We generalize the chimney model by introducing nonlinear restoring and gravitational forces for the purpose of modeling swaying of trees at high wind speeds. We have derived general equations governing the system using Lagrangian formulation. We have studied the simplest case of a single element in more detail. The governing equation we arrive at for this case has not been studied so far. We study the chaotic properties of this simple building block and also the effect of directionality in the wind on the chaotic properties. We also consider the special case of two elements.

nlin.CD↗

arXiv2017

Multifractal invariant measures in expanding piecewise linear coupled maps

We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they become multifractal as soon as two of them are coupled nonlinearly even with a small coupling. For some maps, the multifractal spectrum seems to be robust with the coupling or map parameters and for some other maps, there is a substantial variation. The origin of the multifractal spectrum here is intriguing as it does not seem to conform to the existing theory of multifractal functions.

nlin.CD↗

arXiv2015

Separable local fractional differential equations

The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators naturally incorporate the fractal sets into the equations. Here, the scope of these equations has been extended further by considering different possibilities for the known function. We have also studied a separable local fractional differential equation along with its method of solution.

math-ph↗

arXiv2014

Effect of heat source on the growth of dendritic drying patterns

Shining a tightly-focused but low-powered laser beam on an absorber dispersed in a biological fluid gives rise to spectacular growth of dendritic patterns. These result from localized drying of the fluid because of efficient absorption and conduction of optical energy by the absorber. We have carried out experiments in several biologically relevant fluids and have analyzed patterns generated by different types of absorbers. We observe that the growth velocity of branches in the dendritic patterns can decrease below the value expected for natural drying.

cond-mat.soft↗

arXiv2014

Characterization of the irregularity of a terrain using fractal dimension of lakes' boundaries

Even though many objects and phenomena of importance in geophysics have been shown to have fractal character, there are still many of them which show self-similar character and yet to be studied. The objective of the present work is to demonstrate that the fractal dimension of the boundary of a natural water body can be used to shed light on irregularity as well as other properties of a region. Owing to easy availability of satellite images and image processing softwares this turns out to be a handy tool. In this study, we have analyzed several lakes in India mostly around the Western Ghats region. We find that the fractal dimension of their boundaries for the length scales between around 40 meters to 2 kilometers, in general, has broad variation from 1.2 to 1.6. But when they are grouped into three categories, viz., lakes along the ridge of Western Ghats, lakes in the planes and lakes in the mountain region, we find the first two groups to have a narrower distribution of dimensions.

physics.geo-ph↗

arXiv2014

A simple method to estimate fractal dimension of mountain surfaces

Fractal surfaces are ubiquitous in nature as well as in the sciences. The examples range from the cloud boundaries to the corroded surfaces. Fractal dimension gives a measure of the irregularity in the object under study. We present a simple method to estimate the fractal dimension of mountain surface. We propose to use easily available satellite images of lakes for this purpose. The fractal dimension of the boundary of a lake, which can be extracted using image analysis softwares, can be determined easily which gives the estimate of the fractal dimension of the mountain surface and hence a quantitative characterization of the irregularity of the topography of the mountain surface. This value will be useful in validating models of mountain formation

physics.geo-ph↗

arXiv2013

Recursive Local Fractional Derivative

The definition of the local fractional derivative has been generalised to the orders beyond the critical order. This makes it possible to retain more terms in the local fractional Taylor expansion leading to better approximation. This also extends the validity of the product rule.

nlin.CD↗

arXiv2013

Local Fractional Calculus: a Review

The purpose of this article is to review the developments related to the notion of local fractional derivative introduced in 1996. We consider its definition, properties, implications and possible applications. This involves the local fractional Taylor expansion, Leibnitz rule, chain rule, etc. Among applications we consider the local fractional diffusion equation for fractal time processes and the relation between stress and strain for fractal media. Finally, we indicate a stochastic version of local fractional differential equation.

nlin.CD↗

arXiv2010

STDP-driven networks and the \emph{C. elegans} neuronal network

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of \emph{C. elegans} and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.

q-bio.NC↗

arXiv2008

Evolution of network structure by temporal learning

We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the paradigm of spike-time-dependent plasticity. This incorporates necessary competition between different edges. The final network we obtain is robust and has a broad degree distribution.

nlin.CD↗

arXiv2005

Global Analysis of Synchronization in Coupled Maps

We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two symmetrically coupled tent maps, we also treat the case of two asymmetrically coupled tent maps as well as a globally coupled network. Our main result is the identification of the precise value of the coupling parameter where the synchronizing and desynchronizing transitions take place.

nlin.CD↗

arXiv2005

Brownian motion of fractal particles: Levy flights from white noise

We generalise the Langevin equation with Gaussian white noise by replacing the velocity term by a local fractional derivative. The solution of this equation is a Levy process. We further consider the Brownian motion of a fractal particle, for example, a colloidal aggregate or a biological molecule and argue that it leads to a Levy flight. This effect can also be described using the local fractional Langevin equation. The implications of this development to other complex data series are discussed.

cond-mat.stat-mech↗

arXiv2005

Fractal Stationary Density in Coupled Maps

We study the invariant measure or the stationary density of a coupled discrete dynamical system as a function of the coupling parameter ε(0 < ε< 1/4). The dynamical system considered is chaotic and unsynchronized for this range of parameter values. We find that the stationary density, restricted on the synchronization manifold, is a fractal function. We find the lower bound on the fractal dimension of the graph of this function and show that it changes continuously with the coupling parameter

nlin.CD↗

arXiv1998

Definition of fractal measures arising from fractional calculus

It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable constructions does offer such a possibility. This makes it necessary to have a definition of fractal measures based on the fractional calculus so that the fractals can be naturally incorporated in the calculus. With this motivation a definition of fractal measure has been systematically developed using the concepts of fractional calculus. It has been demonstrated that such a definition naturally arises in the solution of an equation describing diffusion in fractal time.

chao-dyn↗

arXiv1998

Studies of fractal structures and processes using methods of fractional calculus

The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are introduced which involve LFD and one example, local fractional Fokker-Planck equation, is studied in detail.

chao-dyn↗

arXiv1998

Disordered Totally Asymmetric Simple Exclusion Process: Exact Results

We study the effect of quenched spatial disorder on the current-carrying steady states of the totally asymmetric simple exclusion process with spatially disordered jump rates. The exact analytical expressions for the steady-state weights, and the current are found for this model in one dimension. We demonstrate how these solutions can be exploited to study analytically the exact symmetries of the system. In particular, we prove that the magnitude of the steady-state current is left invariant when the direction of all the allowed particle jumps are reversed. Or equivalently, we prove that for any given filling and disorder configuration, particle-hole transformation is an exact symmetry that leaves the steady-state current invariant. This non-trivial symmetry was recently demonstrated in numerical simulations by Tripathy & Burma (preprint cond-mat/9711302).

cond-mat.stat-mech↗