arXiv subjects

Parth Pratim Pandey

Publications and source records attributed to Parth Pratim Pandey.

3 recordsLinked to original sources

arXiv2025

A Mathematical Model to Capture Urbanization Trajectory Induced by Economic Inequality

Analysis of the urban population fraction data for sixteen populous countries over the last fifty years reveals a universal increase in urbanization, exhibiting four qualitatively distinct temporal patterns: (i) continuously accelerating growth, (ii) continuously decelerating growth, (iii) two-phase growth transitioning from acceleration to deceleration, and (iv) two-phase growth transitioning from deceleration to acceleration. To understand the origin of these diverse urbanization trajectories, we develop a simple coarse-grained model in which a country is segregated into two regions, a rural and an urban region. Population in each region evolves due to natural (sexual) growth and migration from rural to urban areas, with the migration rate governed by economic inequality, quantified through the difference in GDP per capita between the two regions. The GDP per capita of both regions is assumed to grow exponentially with distinct rates. We demonstrate that this minimal model, involving four dynamical variables and a small number of demographic and economic parameters, is capable of reproducing all four empirically observed urbanization patterns. Assuming demographic and economic parameters remain approximately constant over a 50-year timescale, we estimate coarse-grained parameters for the United States using empirical data and obtain optimized values that accurately reproduce its observed urbanization trajectory. Our results highlight how simple demographic-economic interactions can generate rich and diverse urbanization dynamics.

physics.soc-ph↗

arXiv2025

Division Strategies Determine Growth and Viability of Growing-Dividing Autocatalytic Systems

We present a geometric framework to study the growth-division dynamics of cells and protocells, and demonstrate that self-reproduction emerges only when a system's growth dynamics and division strategy are mutually compatible. Using several commonly used models (the linear Hinshelwood cycle and non-linear coarse-grained models of protocells and bacteria), we show that, depending on the chosen division mechanism, the same chemical system can exhibit either (i) balanced exponential growth, (ii) balanced nonexponential growth, or (iii) system death (where the system either diverges to infinity or collapses to zero over successive generations). In particular, we show that cellular trajectories in an N-dimensional phase space (where N is the number of distinct chemical species) shuttle between two N-1 dimensional surfaces - a division surface and a birth surface - and that the relationship between these surfaces and the growth trajectories determine something as fundamental as cellular homeostasis and self-reproduction. Geometrically visualizing bacterial growth and division uncovers, for the first time, the type of division processes that sustain or destroy cellular homeostasis in autocatalytic chemical systems, thereby offering strategies to stabilize or destabilize growing-dividing systems. This reveals that, in addition to autocatalysis of growth, division mechanisms are not passive bystanders but active determinants of a growing-dividing system's long-term fate. Our work thus provides a framework for further exploration of growing dividing systems that will aid in the design of self-reproducing synthetic cells.

nlin.AO↗

arXiv2019

Multistability and regime shifts in microbial communities explained by competition for essential nutrients

Microbial communities routinely have several possible species compositions or community states observed for the same environmental parameters. Changes in these parameters can trigger abrupt and persistent transitions (regime shifts) between such community states. Yet little is known about the main determinants and mechanisms of multistability in microbial communities. Here we introduce and study a resource-explicit model in which microbes compete for two types of essential nutrients. We adapt game-theoretical methods of the stable matching problem to identify all possible species compositions of a microbial community. We then classify them by their resilience against three types of perturbations: fluctuations in nutrient supply, invasions by new species, and small changes of abundances of existing ones. We observe multistability and explore an intricate network of regime shifts between stable states in our model. Our results suggest that multistability requires microbial species to have different stoichiometries of essential nutrients. We also find that balanced nutrient supply promote multistability and species diversity yet make individual community states less stable.

q-bio.PE↗