arXiv subjects

Santanu Nandi

Publications and source records attributed to Santanu Nandi.

6 recordsLinked to original sources

arXiv2026

Studying the seismic activity of the earthquake in India using fractal analysis

Natural disaster strikes at any given moment from seemingly out of nowhere Akin to earthquake that strongly affects human with different magnitudes through the course of time. The main aim of this study is the fractal analysis of seismic activity data of India in the interval from 04-10-2016 to 31-05-2023. This includes analyzing the earthquake magnitudes and their epicenters using fractal statistics, which were studied at different scales to identify patterns in the data through the use of the fractal spectrum. The probabilities of future earthquakes with different magnitudes were estimated using the fractal model.

physics.geo-ph↗

arXiv2026

Study of Air Pollution Impact on Human Health in Major Cities in India using Fractal Analysis

This study aims to examine the historical air pollution data from major Indian cities using fractal analysis to measure environmental risk. The fractal dimension of the major air pollutants is computed to evaluate the volatility and complexity of air quality patterns in Delhi, Kolkata, Mumbai, and Bengaluru. Fractal statistics is applied to analyze the fractal spectrum for each region, and further divided into different scales to capture the variation in air quality behaviour. This analysis reveals distinct fractal patterns for each city, showing different levels of environmental instability. These findings make fractal analysis a valuable tool for comparing air quality dynamics. This study offers a new way to measure changes in air quality, helping policymakers create targeted solutions for each city.

math.DS↗

arXiv2026

Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile

We develop a framework for detecting regime transitions in dynamical systems using the Mixup Euler Characteristic Profile (Mixup ECP) -- the Euler characteristic of the geometric intersection of ball unions around adjacent delay-embedded trajectory segments, viewed as a function of filtration scale. The Mixup ECP provides a detection statistic with a built-in null and guaranteed stability. We formalize regime detection as a low-side-permutation test, establish its validity and consistency, and introduce a multi-delay extension that automatically selects the most informative dynamical timescale. Complementing the topological signal with Complexity Variance, Higuchi fractal dimension, and a rolling mean baseline, the four-signal combined method achieves $9.50$ days MAE on Indian monsoon onset (Nepal target) -- a $32\%$ improvement over the rolling mean baseline and $9\%$ over CUSUM. Validated on the Lorenz system, logistic map, and three monsoon systems spanning both hemispheres (Indian/Nepal, Indian/Kerala, Western North Pacific), plus ENSO and a synthetic EEG dataset, the framework adds value precisely when the transition is gradual or obscured by noise.

math.DS↗

arXiv2022

On Dynamics of λ+ tan z^2

This article discusses some topological properties of the dynamical plane ($z$-plane) of the holomorphic family of meromorphic maps $λ+ \tan z^2$ for $ λ\in \mathbb C$. In the dynamical plane, we prove that there is no Herman ring, and the Julia set is a Cantor set for the maps when the parameter is in the unbounded hyperbolic component contained in the four quadrants in the complex plane. Julia set is connected for the maps when the parameters are in other hyperbolic components of the parameter plane.

math.DS↗

arXiv2020

Combinatorial structure of the parameter plane of the family $\lambda \tan z^2$

In this article we will discuss combinatorial structure of the parameter plane of the family $ \mathcal F = \{ \lambda \tan z^2: \lambda \in \mathbb C^*, \ z \in \mathbb C\}.$ The parameter space contains components where the dynamics are conjugate on their Julia sets. The complement of these components is the bifurcation locus. These are the hyperbolic components where the post-singular set is disjoint from the Julia set. We prove that all hyperbolic components are bounded except the four components of period one and they are all simply connected.

math.DS↗

arXiv2020

Dynamics of the family $\lambda$ tangent $z^2$

This article discusses some topological properties of the dynamical plane ($z$-plane) of the holomorphic family of meromorphic maps $\lambda \tan z^2$ for $ \lambda \in \mathbb C^*$. In the dynamical plane, I prove that there is no Herman ring and the Julia set is a Cantor set for the maps when the parameter is in the hyperbolic component containing the origin. Julia set is connected for the maps when the parameters are in other hyperbolic components in the parameter plane.

math.DS↗