arXiv subjects

Martin Hendrick

Publications and source records attributed to Martin Hendrick.

6 recordsLinked to original sources

arXiv2026

Disorder Crossover in Urban-Front Growth

Urban expansion fronts display a robust local roughness exponent together with strongly dispersed growth and nonuniversal dynamic exponents. We show that this coexistence can arise from a disorder-controlled crossover in projected-front growth. Introducing a minimal Eden model, in which geographic constraints act as quenched dilution and coalescence as quenched local acceleration, we demonstrate that the resulting front enters a long disorder-dominated preasymptotic regime, whose scaling near threshold is set by ordinary two-dimensional percolation. In this regime, the local roughness remains close to $1/2$, while the large-scale exponents vary broadly with disorder and acceleration. These results provide a minimal explanation of urban-front roughening and suggest a more general mechanism for stochastic growth in heterogeneous media.

physics.soc-ph↗

arXiv2026

Mobility shapes heat exposure inequalities in cities

Segregation has long been recognized as a driver of environmental inequalities, with disadvantaged groups often living in neighborhoods where heat-related risks are highest. Yet, it remains unclear how daily mobility patterns, embedded within heterogeneous urban heat fields, shape heat exposure inequalities across sociodemographic groups. Using mobile phone records of daily mobility flows and urban temperature fields across 23 Spanish cities, we develop a network-based framework to quantify how different sociodemographic groups experience heat through their daily movements. We further apply the framework to tract-level commuting networks across 30 major US cities as an external validation, yielding qualitatively comparable patterns. We find systematic income-related inequalities, with low-income groups consistently experiencing higher exposure than high-income groups, while age-related disparities are smaller in magnitude. These inequalities intensify during commuting trips, indicating that routine mobility amplifies spatial heat gradients more than non-routine movements. Finally, we show that parsimonious population-based mobility models with group-agnostic mobility rules reproduce an important component of the observed exposure disparities, suggesting that these inequalities emerge from the interplay between the unequal spatial organization of daily activities across sociodemographic groups and urban heat gradients. Our findings provide a generalizable framework to characterize inequalities in mobility-based heat exposure across cities and inform climate-resilient urban planning and public health strategies under intensifying climate-related risks.

physics.soc-ph↗

arXiv2025

Dynamic roughening of cities driven by multiplicative noise

The evolution of urban landscapes is rapidly altering the surface of our planet. Yet, our understanding of the urbanisation phenomenon remains far from complete. A fundamental challenge is to describe spatiotemporal changes in the built environment. A dynamic theory of urban evolution should account for both vertical and horizontal city expansion, analogous to the dynamical behaviour of surface growth in physical and biological systems. Here we show that building-height dynamics in cities around the world are well described by a zero-dimensional geometric Brownian motion (GBM), where multiplicative noise drives stochastic fluctuations around a deterministic drift associated with economic growth. To account for intra-city correlations, we extend the GBM with spatial coupling, revealing how local interactions effectively mitigate noise-driven fluctuations and shape urban morphology. The continuum limit of this spatial model can be recasted into the Kardar-Parisi-Zhang (KPZ) equation and we find that empirical estimates of the roughness exponent are in the range of the KPZ prediction for most cities. Together, these results show that multiplicative noise, moderated by local interactions, governs the evolution of urban roughness, anchoring spatiotemporal city dynamics in a well-established statistical physics framework.

physics.soc-ph↗

arXiv2025

Scaling intra-urban climate fluctuations

Urban-induced microclimate variations, such as urban heat islands and air pollution, scale with city size, producing distinctive relations between average climate variables and city-scale quantities (e.g., total population). However, these relations are sensitive to city boundary definitions and overlook intra-urban variability. Here, we overcome these limitations by using high-resolution data of urban temperatures, air quality, population, and street networks from 142 cities worldwide, showing that their marginal and joint probability distributions collapse onto a set of general functions inspired by finite-size scaling in statistical physics. Through a logarithmic relation linking urban spatial features to climate variables, we find that average street network properties are sufficient to characterize the full variability of temperature and air pollution fields within and across cities. These findings show that intra-urban climate variability follows general scaling functions, enabling the integration of climate information into reduced-complexity models of urban systems to better inform future urban planning.

physics.soc-ph↗

arXiv2019

Can Local Stress Enhancement Induce Stability in Fracture Processes? Part I: Apparent Stability

By comparing the evolution of the local and equal load sharing fiber bundle models, we point out the paradoxical result that stresses seem to make the local load sharing model stable when the equal load sharing model is not. We explain this behavior by demonstrating that it is only an apparent stability in the local load sharing model, which originates from a statistical effect due to sample averaging. Even though we use the fiber bundle model to demonstrate the apparent stability, we argue that it is a more general feature of fracture processes.

cond-mat.dis-nn↗

arXiv2018

Mesoscopic Description of the Equal Load Sharing Fiber Bundle Model

One aim of the equal load sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this, is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the critical behavior found through recursive dynamics. It allows us to link the model with the unifying framework of absorbing phase transitions traditionally used in the study of non-equilibrium phase transitions. Moreover, it highlights the analogy between equal load sharing and spinodal nucleation. Consequently, this work is a first step towards the quest of a field theory for fiber bundle models.

cond-mat.stat-mech↗