We propose a scaling equation describing transport properties (diffusion and viscosity) in the solutions of colloidal particles. We apply the equation to 23 different systems including colloids and proteins differing in size (range of diameters: 4 nm to 1 μm), and volume fractions (10(-3)-0.56). In solutions under study colloids/proteins interact via steric, hydrodynamic, van der Waals and/or e...

We study a social network consisting of over 10(4) individuals, with a degree distribution exhibiting two power scaling regimes separated by a critical degree k(crit), and a power law relation between degree and local clustering. We introduce a growing random model based on a local interaction mechanism that reproduces the observed scaling features and their exponents. We suggest that the doubl...

We subjected the time series of quasi-rigid-body vibration pulses (elastic emissions) from laboratory fracture carried out by a piezoelectric accelerometer on concrete and rock specimens under uniaxial compression to statistical analysis. In both cases, we find that the waiting-time distribution can be described by a scaling law extending over several orders of magnitude. This law is indistingu...

We survey scaling arguments, both asymptotic (involving regular variation) and exact (involving self-similarity), in various areas of mathematical analysis and mathematical physics. 1. Scaling and Fechner’s law There is a sizeable body of theory to the effect that, where two related physically meaningful functions f and g have no natural scale in which to measure their units, and are reasonably...

We analyze particle diffusion and edge emittance growth induced by discreteparticle effects in two-dimensional self-consistent simulation studies of beam dynamics. In particular, an analytical model is presented which describes the slow-time-scale evolution of the edge emittance of a perfectly matched beam in a periodic solenoidal magnetic field. A scaling law for edge emittance growth is deriv...

We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a scaling appropriate for such power-law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-level kernel that determines all eigenvalue correlations. We show that such ensembles belong t...

We study the dynamics of an intriguing crossover from a chaotic to a power-law state as a function of strain rate within the context of a recently introduced model that reproduces the crossover. While the chaotic regime has a small set of positive Lyapunov exponents, interestingly, the scaling regime has a power-law distribution of null exponents which also exhibits a power law. The slow-manifo...

We review the application of renormalization group (RG) methods to the problem of isotropic turbulence, with attention to Kolmogorov’s phenomenological scaling law. We see that RG reproduces the form of the 5/3 law and can also be used to obtain estimates of the Kolmogorov constant that agree with experiment and numerical simulation. The articles reviewed also confirm the universality of the sc...

Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible growth model for critical systems and deduce constraints in their growth : the well-known preferential attachment principle, and, mainly, a new law of temporal...

We consider the deformation of a thin elastic film bonded to a thick compliant substrate, when the (compressive) misfit is far beyond critical. We take a variational viewpoint – focusing on the total elastic energy, i.e. the membrane and bending energy of the film plus the elastic energy of the substrate – viewing the buckling of the film as a problem of energy-driven pattern formation. We iden...