Related papers: Flow similarity, stochastic branching, and quarter…
Power law distributions have been repeatedly observed in a wide variety of socioeconomic, biological and technological areas. In many of the observations, e.g., city populations and sizes of living organisms, the objects of interest evolve…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
Living systems continuously transform matter and energy through the chemical processes that constitute their metabolism. The overall metabolic rate of an organism correlates positively with its body mass, however both the exact scaling…
Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales with brain volume raised to a power of around 5/6. This value is significantly higher than the more common exponent 3/4 relating whole body…
Scientists have long sought to understand how vascular networks supply blood and oxygen to cells throughout the body. Recent work focuses on principles that constrain how vessel size changes through branching generations from the aorta to…
Domain branching near the boundary appears in many singularly-perturbed models for microstructure in materials and was first demonstrated mathematically by Kohn and M\"uller for a scalar problem modeling the elastic behavior of shape-memory…
The ubiquitous $3/4$ metabolic scaling exponent, known as Kleiber's law, has long been attributed to the minimization of viscous dissipation within fractal transport networks. In this paper, we invert this standard narrative, demonstrating…
Networks of interconnected materials permeate throughout nature, biology, and technology due to exceptional mechanical performance. Despite the importance of failure resistance in network design and utility, no existing physical model…
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…
With the number of fully-sequenced genomes now well over a hundred it has become possible to start investigating if there are any quantitative regularities in the genetic make-up of genomes. In (physics/0307001), I originally showed that…
Production of energy (metabolism) and its distribution is vital for living organisms, both at individual level - between different functions of an organism, as well as between species of communities at different organizational levels,…
A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a new model is proposed which includes breakable…
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average…
A longstanding problem in biology has been the origin of pervasive quarter-power allometric scaling laws that relate many characteristics of organisms to body mass (M) across the entire spectrum of life from molecules and microbes to…
We extend a previously theory for the interspecific allometric scaling developed in a $d+1$-dimensional space of metabolic states. The time, which is characteristic of all biological processes, is included as an extra dimension to $d$…
This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but…
Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…
Understanding how annual peak flow, $Q_p$, relates to upstream basin area, $A$, and their scaling have been one of the challenges in surface hydrology. Although a power-law scaling relationship (i.e., $Q_p \propto A^\alpha$) has been widely…
Plants solve complex problems without centralized control, relying instead on growth-driven dynamics to sense, navigate, and optimize resource acquisition. This review presents a unified physical framework for understanding plant behavior…
Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles,…