We address the branching of magnetic domains in a uniaxial ferromagnet. Our thesis is that branching is required for a domain pattern to have nearly{minimal energy. To show this, we consider the nonlocal, nonconvex variational problem of micromagnetics. We identify the scaling law of the minimum energy, by proving a rigorous lower bound which matches the already-known upper bound. We further sh...

We analyzed the statistical distribution of intra-specific local abundances for a set North American breeding bird species. We constructed frequency plots for every species and found that they showed long-tail power-law behavior, truncated at an upper abundance cut-off value. Based on finite size scaling arguments, we investigated whether frequency curves may be considered scaled copies of each...

We report a joint experimental and theoretical investigation of cyclic training of amorphous frictional granular assemblies, with special attention to memory formation and retention. Measures of dissipation and compactification are introduced, culminating with a proposed scaling law for the reducing dissipation and increasing memory. This scaling law is expected to be universal, insensitive to ...

We ask whether statistical averages in chaotic systems can be computed or measured reliably under the influence of noise. Situations are identified where the invariance of such averages breaks down as the noise amplitude increases through a critical level. An algebraic scaling law is obtained which relates the change of the averages to the noise variation. This breakdown of shadowability of sta...

It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such sample space reducing processes offer an alternative newmechanism to understand the emergence of scaling in countless processes. The corresponding power law exponents were shown to be related...

The aim of this paper is to extend our knowledge about the power-law relationship between citationbased performance and collaboration patterns for papers in the natural sciences. We analyzed 829,924 articles that received 16,490,346 citations. The number of articles published through collaboration account for 89%. The citation-based performance and collaboration patterns exhibit a power-law cor...

We use molecular dynamics simulation results on viscous binary Lennard-Jones mixtures to examine the correlation between the potential energy and the virial. In accord with a recent proposal [U. R. Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)], the fluctuations in the two quantities are found to be strongly correlated, exhibiting a proportionality constant, Gamma, numerically equal to o...

We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behavior can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the finitesize scaling analysis. The relation between order parameter, criticality and scaling law of fluctuations has been established and the connexion between ...

Tornadoes cause loss of life and damage to property each year in the United States and around the world. The largest impacts come from 'outbreaks' consisting of multiple tornadoes closely spaced in time. Here we find an upward trend in the annual mean number of tornadoes per US tornado outbreak for the period 1954-2014. Moreover, the variance of this quantity is increasing more than four times ...

This letter investigates the energy efficiency (EE) scaling law for the broadcasting channels (BC) with many users, in which the non-ideal transmit independent power consumption is taken into account. We first consider the single antenna case with K users, and derive that the EE scales as log2 lnK α when α > 0 and log2 K when α = 0, where α is the normalized transmit independent power. After th...