Related papers: Beyond Murray's Law: Non-Universal Branching Expon…
The branching geometry of biological transport networks is characterized by a diameter scaling exponent $\alpha$. Two structural attractors compete: impedance matching ($\alpha \sim 2$) for pulsatile flow and viscous-metabolic minimization…
The branching behavior of vascular trees is often characterized using Murray's law. We investigate its validity using synthetic vascular trees generated under global optimization criteria. Our synthetic tree model does not incorporate…
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,…
Why does the mammalian vascular tree maintain a conserved branching exponent $\alpha^* \approx 2.72$ across a $10^7$-fold range in body mass, despite a fundamental shift from viscous to wave-dominated transport? We prove this universality…
Murray's theory of constrained minimum-power branchings is critically reviewed in a generalised framework for a range of cases: channels with arbitrary cross-section shape, laminar flows of Newtonian and non-Newtonian fluids, and low and…
Murray-type flux-radius laws, Gilbert-type concave transport costs, and Young-Herring triple-junction angle balances are usually treated as separate theories. This work shows that, within a natural class of quadratic, scale-free ledgers for…
A central debate in biology has been the allometric scaling of metabolic rate. Kleiber's observation that animals' basal metabolic rate scales to the 3/4-power of body mass (Kleiber's rule) has been the prevailing hypothesis in the last…
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…
It is shown that, in the scaling regime, transport properties of quantum wires with off-diagonal disorder are described by a family of scaling equations that depend on two parameters: the mean free path and an additional continuous…
We have investigated scaling properties of the Aubry-Andr\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground…
Recently, West et al. claimed to derive a general quantitative model based on fundamental principles for the allocation of metabolic energy between maintenance of existing tissue and the production of new biomass, and in addition claimed to…
We examine the scaling law $B \propto M^{\alpha}$ which connects organismal metabolic rate $B$ with organismal mass $M$, where $\alpha$ is commonly held to be 3/4. Since simple dimensional analysis suggests $\alpha=2/3$, we consider this to…
This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler-Maxwell system with collisions when initial data are around a constant equilibrium state. The main goal is the rigorous…
A general simple theory for the interspecific allometric scaling is developed in the $d+1$-dimensional space ($d$ biological lengths and a physiological time) of metabolic states of organisms. It is assumed that natural selection shaped the…
Allometry or the quantitative study of the relationship of body size to living organism physiology is an important area of biophysical scaling research. The West-Brown-Enquist (WBE) model of fractal branching in a vascular network explains…
Meaningful laws of nature must be independent of the units employed to measure the variables. The principle of similitude (Rayleigh 1915) or dimensional homogeneity, states that only commensurable quantities (ones having the same dimension)…
One major open conjecture in the area of critical random graphs, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade [23, 24, 28, 63] is as follows: for a wide array of random…
When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such…
We investigate a driven particle system, a multilane asymmetric exclusion process, where the particle number in every lane is conserved, and stationary state is fully uncorrelated. The phase space has, starting from three lanes and more, an…
We use a bifurcation theory due to Crandall and Rabinowitz to show the existence of a symmetry breaking bifurcation of a specific one parameter family of axially symmetric disc type solutions of a membrane equation with fixed boundary. In…