Related papers: From dynamical scaling to local scale-invariance: …
We extend the theory of non-thermal fixed points to the case of anomalously slow universal scaling dynamics according to the sine-Gordon model. This entails the derivation of a kinetic equation for the momentum occupancy of the scalar field…
Using Wilson renormalization group, we show that if no integrated vector operator of scaling dimension $-1$ exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schr\"odinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The…
We consider cascade models of turbulence which are obtained by restricting the Navier-Stokes equation to local interactions. By combining the results of the method of extended self-similarity and a novel subgrid model, we investigate the…
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical…
A nonlinear generalisation of Schrodinger's equation is obtained using information-theoretic arguments. The nonlinearities are controlled by an intrinsic length scale and involve derivatives to all orders thus making the equation mildly…
We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete scale invariance. The rich features of this transition characterized by the abrupt formation of a geometric…
We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in a plane. Both a continuous energy with linear growth depending on a measure which characterizes the macroscopic dislocation density and a nonlocal…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…
The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an…
Using numerical simulations we investigate the space-time properties of a system in which spirals emerge within coarsening domains, thus giving rise to non-trivial internal dynamics. Initially proposed in the context of population dynamics,…
A fluid is said to be \emph{scale-invariant} when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale invariance provides a dynamical symmetry…
The approach to equilibrium, from a nonequilibrium initial state, in a system at its critical point is usually described by a scaling theory with a single growing length scale, $\xi(t) \sim t^{1/z}$, where z is the dynamic exponent that…
An exact solution is introduced for one dimensional space-fractional Edwards-Wilkinson equation. It is shown that the roughness obeys the Family-Viscek dynamic scaling form and the scaling exponents is derived. It is seen that the scaling…
We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the non-diluted…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
Many real-world social networks constantly change their global properties over time, such as the number of edges, size and density. While temporal and local properties of social networks have been extensively studied, the origin of their…
Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form $S = \int L_{1} \Phi d^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where the volume element $\Phi d^4x$ is…
We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters…