Related papers: A framework for crossover of scaling law as a self…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
Scaling laws for characteristic length scales (in time or in the model parameters) are both experimentally robust and accessible for rigorous analysis. In multiscale situations cross--overs between different scaling laws are observed. We…
Complex phenomena incorporating several physical properties are abundant while they are occasionally revealing the variation of power-law behavior depending on the scale. In this present work, the global scaling-behavior of dynamical impact…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
We consider a stochastic sandpile where the sand-grains of unstable sites are randomly distributed to the nearest neighbors. Increasing the value of the threshold condition the stochastic character of the distribution is lost and a…
The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for…
Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based…
We employ molecular dynamics simulations to investigate the domain morphology and growth kinetics of a vapor-liquid system embedded within a complex porous medium. By systematically varying the pore structure, we analyze the scaling…
A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsmooth. For the border-collision normal form in two…
Droplet impacts are fundamental to fluid-structure interactions, shaping processes from erosion to bioprinting. While previous scaling laws have provided insights into droplet dynamics, force scaling laws remain insufficiently understood,…
Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…
We report a new theory of dissipative forces acting between colliding viscoelastic bodies. The impact velocity is assumed not to be large, to avoid plastic deformations and fragmentation at the impact. The bodies may be of an arbitrary…
Wrinkling, creasing and folding are frequent phenomena encountered in biological and man-made bilayers made by thin films bonded to thicker and softer substrates often containing fibers. Paradigmatic examples of the latter are the skin, the…
This study employs molecular dynamics simulations to investigate droplet dynamics when a stationary droplet on a solid surface is struck by another droplet of similar size from above. The focus is on the jumping behavior of the merged…
This paper presents two interesting scaling laws, which relate some critical exponents in the critical behavior of spherically symmetric gravitational collapses. These scaling laws are independent of the details of gravity theory under…
The existence of unique scaling in a crossover regime between viscous and inertial hydrodynamic regimes is revealed for homogeneous, isotropic, incompressible, spinodal turbulence which is characterized, to begin with, by three different…
The aim of this work is to make a further step towards the understanding of the near-critical reflection of internal gravity waves from a slope in the more general and realistic context where the size of viscosity $\nu$ and the size of…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
We study the crossover from self--similar scaling behavior to asymptotically self--affine (anisotropic) structures. As an example, we consider bond percolation with one preferred direction. Our theory is based on a field--theoretical…
We study models of interacting fermions in one dimension to investigate the crossover from integrability to non-integrability, i.e., quantum chaos, as a function of system size. Using exact diagonalization of finite-sized systems, we study…