arXiv subjects

Nirbhay Patil

Publications and source records attributed to Nirbhay Patil.

6 recordsLinked to original sources

arXiv2026

The role of nestedness and saturating feedback in bipartite ecological systems

Large ecosystems balance competition and cooperation, yet standard generalized Lotka--Volterra models make mutualism destabilizing by amplifying disorder and driving unbounded growth. We show that Monod-like saturation resolves this paradox: dynamical mean-field theory and random-matrix analysis reveal a broader stable phase and enhanced survival. Network architecture provides a second control mechanism, but nestedness offers no intrinsic stability advantage. Instead, it is a byproduct of degree distributions with high connectivity necessary for stability.

q-bio.PE↗

arXiv2026

Dynamical systems on ultra small-world networks

Despite the knowledge that social, economical, and ecological networks are often of a small-world nature with inter-nodal distance growing even slower than logarithmically with system size, we often assume theoretical systems to be outside of this regime, to make them easier to treat analytically. Here we derive a framework to apply the powerful dynamical mean-field theory on highly heterogeneous networks that is able to account for more of the degree correlations naturally arising from network constraints, known as structural cut-offs. We apply this framework to the well-studied and understood disordered Lotka-Volterra model, and show typically reported observables such as survival rates and stability for these systems on ultra small-world networks. We find much better agreement for these variables for all ranges of exponents for simulated power-law networks as well as empirically sourced networks.

cond-mat.dis-nn↗

arXiv2024

The Spectral Boundary of Block Structured Random Matrices

Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations, generalising the elliptic ensemble. We determine analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes.

cond-mat.dis-nn↗

arXiv2024

Emergent Inequalities in a Primitive Agent-Based Good-Exchange Model

Rising inequalities around the globe bring into question our economic systems and the origin of such inequalities. Here we propose a toy agent-based model where each entity is simultaneously producing and consuming indivisible goods. We find that the system exhibits a non-trivial phase transition beyond which a market clearing equilibrium exists but becomes dynamically unreachable. When production capacity exceeds a threshold and adapts too slowly, some agents cannot sell all their goods. This leads to global price deflation and induces strong wealth inequalities, with the spontaneous separation of the population into a rich class and a poor class. We explore ways to alleviate poverty in this model and whether they have real life significance.

cond-mat.dis-nn↗

arXiv2023

Income Inequalities Increase with City Size: Evidence from French Data

We analyse the income distributions of cities in France and the scaling of the income of different deciles as a function of the population. We find a significant difference in the scaling exponents for the richer and poorer parts of the population, implying an unequivocal rise in inequalities in larger cities, made worse by living costs that are disproportionately higher for the poor. We find that the distribution of revenues of cities in France has a universal, Gumbel-like form, with mean and variance growing with the logarithm of population. We show how this result directly implies different income scaling exponents as a function of decile. We also study the spatial correlations of income and population, which decay exponentially with distance. We find that large cities are not more income-segregated than small cities. Finally, we search for couplings between social and economic factors, like age and income, and propose a toy model that reproduces some of our observations.

physics.soc-ph↗

arXiv2020

Mitochondrial cristae modeled as an out-of-equilibrium membrane driven by a proton field

As the places where most of the fuel of the cell, namely ATP, is synthesized, mitochondria are crucial organelles in eukaryotic cells. The shape of the invaginations of the mitochondria inner membrane, known as cristae, has been identified as a signature of the energetic state of the organelle. However, the interplay between the rate of ATP synthesis and the crista shape remains unclear. In this work, we investigate the crista membrane deformations using a pH-dependent Helfrich model, maintained out-of-equilibrium by a diffusive flux of protons. This model gives rise to shape changes of a cylindrical invagination, in particular to the formation of necks between wider zones under variable, and especially oscillating, proton flux.

physics.bio-ph↗