相关论文: Spinodal Decomposition and the Tomita Sum Rule
We discuss the scaling exponents characterizing the power-law behavior of the anisotropic components of correlation functions in turbulent systems with pressure. The anisotropic components are conveniently labeled by the angular momentum…
It remains an open problem if there are universal scaling functions across a topological quantum phase transition (TPT) without an order parameter, but with extended Fermi surfaces (FS ). Here, we study a simple system of fermions hopping…
The chiral expansion of the low energy processes $\pi^0\to\gamma\gamma$ and $\eta\to\gamma\gamma$ is reconsidered with particular emphasis on the question of the evaluation of the two low-energy parameters from ${\cal L}^{WZ}_{(6)}$ which…
Dynamical scaling in ageing systems, notably in phase-ordering kinetics, is well-established. New evidence in favour of Galilei-invariance in phase-ordering kinetics is reviewed.
A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the…
Scaling and universality in the Ohmic two-state system is investigated by exploiting the equivalence of this model to the anisotropic Kondo model. For the Ohmic two-state system, we find universal scaling functions for the specific heat,…
The a priori error analysis of reduced order models (ROMs) for fluids is relatively scarce. In this paper, we take a step in this direction and conduct numerical analysis of the recently introduced time relaxation ROM (TR-ROM), which uses…
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…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
A simple scaling theory for the sintering of fractal aerogels is presented. The densification at small scales is described by an increase of the lower cut-off length $a$ accompanied by a decrease of the upper cut-off length $\xi$, in order…
The one-dimensional $O(2)$ model is the simplest example of a system with topological textures. The model exhibits anomalous ordering dynamics due to the appearance of two characteristic length scales: the phase coherence length, $L \sim…
Dislocation systems exhibit well known scaling properties such as the Taylor relationship between flow stress and dislocation density, and the "law of similitude" linking the flow stress to the characteristic wavelength of dislocation…
This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed,…
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…
Many materials quenched into their ordered phase undergo ageing and there show dynamical scaling. For any given dynamical exponent z, this can be extended to a new form of local scale-invariance which acts as a dynamical symmetry. The…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
A previous analysis of scaling, bounds, and inequalities for the non-interacting functionals of thermal density functional theory is extended to the full interacting functionals. The results are obtained from analysis of the related…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…
The leading correction to scaling associated with departures of the initial condition from the scaling morphology is determined for some soluble models of phase-ordering kinetics. The result for the pair correlation function has the form…