Related papers: Statistical hydraulic model for the Leonardo's rul…
Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar…
The vascular network of leaves, comprising xylem and phloem, is a highly optimized system for the delivery of water, nutrients, and sugars. The design rules for these naturally occurring networks have been studied since the time of Leonardo…
A Monte Carlo method based on a density-of-states sampling is proposed for study of arbitrary statistical mechanical ensembles in a continuum. A random walk in the two-dimensional space of particle number and energy is used to estimate the…
The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper we show that a thermodynamic model based on the Maximum Entropy Principle, with dynamical prior information, can be constructed that…
Shape is one of the important characteristics for the structures observed in living organisms. Whereas biologists have proposed models where the shape is controlled on a molecular level [1], physicists, following Turing [2] and d'Arcy…
Liquids in contact with solids are submitted to intermolecular forces inferring density gradients at the walls. The van der Waals forces make liquid heterogeneous, the stress tensor is not any more spherical as in homogeneous bulks and it…
In Amazing numbers in biology, Flindt reports a giant, 128 meter-tall eucalyptus, and a 135 meter-tall sequoia. However, the explanation of the maximum altitude of the crude sap ascent and consequently the main reason of the maximum size…
Based on the three rules developed from the Roe-type scheme, the mechanisms of the classical and preconditioned Harten-Lax-van Leer (HLL) schemes are analyzed. For the classical HLL scheme, the accuracy problem is attributable to the…
Many networked systems such as electric networks, the brain, and social networks of opinion dynamics are known to obey conservation laws. Examples of this phenomenon include the Kirchoff laws in electric networks and opinion consensus in…
Biodiversity monitoring represents a pressing global priority, and assessing forest community composition plays a crucial role due to its influence on ecosystem functions. The spatial distribution of forest species becomes essential for…
For taxonomic levels higher than species, the abundance distributions of number of subtaxa per taxon tend to approximate power laws, but often show strong deviationns from such a law. Previously, these deviations were attributed to…
Understanding the flow dynamics of yield stress fluids in porous media presents a substantial challenge. Both experiments and extensive numerical simulations frequently show a non-linear relationship between the flow rate and the pressure…
The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a…
We use large-scale Monte Carlo simulations to obtain comprehensive results for domain growth and aging in the random field XY model in dimensions $d=2,3$. After a deep quench from the paramagnetic phase, the system orders locally via…
In 1926, Murray proposed the first law for the optimal design of blood vessels. He minimized the power dissipation arising from the trade-off between fluid circulation and blood maintenance. The law, based on a constant fluid viscosity,…
We examine the dynamics of two coalescing liquid drops in the `inertial regime', where the effects of viscosity are negligible and the propagation of the bridge front connecting the drops can be considered as `local'. The solution fully…
Inspired by river networks and other structures formed by Laplacian growth, we use the Loewner equation to investigate the growth of a network of thin fingers in a diffusion field. We first review previous contributions to illustrate how…
We consider a thermodynamic state of a solvent and solution separated with an elastic semipermeable membrane in a box with a constant volume and the relevance of this simple model for the water uptake in tall trees. Under moderate…
The current distribution of language size in terms of speaker population is generally described using a lognormal distribution. Analyzing the original real data we show how the double-Pareto lognormal distribution can give an alternative…
We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate…