Related papers: Dynamics of Cities
Ecosystems and other naturally resilient systems exhibit allometric scaling in the distribution of sizes of their elements. In this paper we define an allometry inspired scaling indicator for cities that is a first step towards quantifying…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
A fundamental question in nonequilibrium statistical physics is whether effective equilibrium behavior can emerge at coarse-grained scales in strongly driven systems. Here, we investigate this question in the context of human mobility by…
We developed a physics-based analytical model to describe the nonlinear mechanical response of aspirated elastic shells. By representing the elastic energy through a stretching modulus, $K$, and a dimensionless ratio, $\delta$, capturing…
Urban growth sometimes leads to rigid infrastructure that struggles to adapt to changing demand. This paper introduces a novel approach, aiming to enable cities to evolve and respond more effectively to such dynamic demand. It identifies…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
Detecting and quantifying non-equilibrium activity is essential for studying internally driven assemblies, including synthetic active matter and complex living systems such as cells or tissue. We discuss a non-invasive approach of measuring…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the…
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
The experimental search for the QCD critical point by means of relativistic heavy-ion collisions necessitates the development of dynamical models of fluctuations. In this work we study the fluctuations of the net-baryon density near the…
The lack of efficiency in urban diffusion is a debated issue, important for biologists, urban specialists, planners and statisticians, both in developed and new developing countries. Many approaches have been considered to measure urban…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
Understanding the physics of nonequilibrium systems remains as one of the major challenges of theoretical physics. This problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing…
We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the…
We present a modelling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments…
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval…
Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…