Kinetic roughening, global quantities, and fluctuation-dissipation relations

Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but that is also directly conjugate to an experimentally accessible parameter, thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions. Exploiting the full analyticity of the linear Edwards-Wilkinson and Mullins-Herring equations, we study in detail various two-time functions related to that quantity. This quantity fulfills the fluctuation-dissipation theorem when considering steady-state equilibrium fluctuations.Comment: 13 pages, 5 figure

The plasmamembrane calmodulin–dependent calcium pump: a major regulator of nitric oxide synthase I

The plasma membrane calcium/calmodulin-dependent calcium ATPase (PMCA) (Shull, G.E., and J. Greeb. 1988. J. Biol. Chem. 263:8646–8657; Verma, A.K., A.G. Filoteo, D.R. Stanford, E.D. Wieben, J.T. Penniston, E.E. Strehler, R. Fischer, R. Heim, G. Vogel, S. Mathews, et al. 1988. J. Biol. Chem. 263:14152–14159; Carafoli, E. 1997. Basic Res. Cardiol. 92:59–61) has been proposed to be a regulator of calcium homeostasis and signal transduction networks of the cell. However, little is known about its precise mechanisms of action. Knock-out of (mainly neuronal) isoform 2 of the enzyme resulted in hearing loss and balance deficits due to severe inner ear defects, affecting formation and maintenance of otoconia (Kozel, P.J., R.A. Friedman, L.C. Erway, E.N. Yamoah, L.H. Liu, T. Riddle, J.J. Duffy, T. Doetschman, M.L. Miller, E.L. Cardell, and G.E. Shull. 1998. J. Biol. Chem. 273:18693–18696). Here we demonstrate that PMCA 4b is a negative regulator of nitric oxide synthase I (NOS-I, nNOS) in HEK293 embryonic kidney and neuro-2a neuroblastoma cell models. Binding of PMCA 4b to NOS-I was mediated by interaction of the COOH-terminal amino acids of PMCA 4b and the PDZ domain of NOS-I (PDZ: PSD 95/Dlg/ZO-1 protein domain). Increasing expression of wild-type PMCA 4b (but not PMCA mutants unable to bind PDZ domains or devoid of Ca2+-transporting activity) dramatically downregulated NO synthesis from wild-type NOS-I. A NOS-I mutant lacking the PDZ domain was not regulated by PMCA, demonstrating the specific nature of the PMCA–NOS-I interaction. Elucidation of PMCA as an interaction partner and major regulator of NOS-I provides evidence for a new dimension of integration between calcium and NO signaling pathways

On logarithmic extensions of local scale-invariance

Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schr\"odinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena.Comment: 23 pages, Latex2e, 2 eps figures included, final form (now also includes discussion of KPZ equation

Dynamics of curved interfaces

Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance principle has been applied. We examine differences and similarities with the classical planar equations. Some characteristic features are the loss of correlation through time and a particular behaviour of the average fluctuations. Dependence on the metric is also explored. The diffusive model that propagates correlations ballistically in the planar situation is particularly interesting, as this propagation becomes nonuniversal in the new regime.Comment: Published versio

Symmetry based determination of space-time functions in nonequilibrium growth processes

We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in 1+1 and in 2+1 space dimensions. This corrects earlier studies which claimed that in 2+1 dimensions the two models belong to different universality classes.Comment: 18 pages, three figures included, submitted to Phys. Rev.

From dynamical scaling to local scale-invariance: a tutorial

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. Schr\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for

Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance

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 branching-annihilating random walk, two exactly solvable particle-reaction models and kinetic growth models. While the generic scaling descriptions known from magnetic system can be taken over, some of the scaling relations between the ageing exponents are no longer valid. In particular, there is no obvious generalization of the universal limit fluctuation-dissipation ratio. The form of the scaling function of the two-time response function is compared with the prediction of the theory of local scale-invariance.Comment: Latex2e with IOP macros, 32 pages; extended discussion on contact process and new section on kinetic growth processe