Related papers: On generalized scaling laws with continuously vary…
Within wall turbulence, there is a sublayer where the mean velocity and the variance of velocity fluctuations vary logarithmically with the height from the wall. This logarithmic scaling is also known for the mean concentration of a passive…
The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating…
We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium…
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random…
Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general…
Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to…
Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At…
The strength of most metals used in daily life scales with either an internal or external length scale. Empirically, this is characterized by power-laws persisting to six orders of magnitude in both strength and length scale. Attempts at…
Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…
It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and…
Scaling-invariant functions preserve the order of points when the points are scaled by the same positive scalar (with respect to a unique reference point). Composites of strictly monotonic functions with positively homogeneous functions are…
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…
The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…