Absorbing boundaries in the conserved Manna model

The conserved Manna model with a planar absorbing boundary is studied in various space dimensions. We present a heuristic argument that allows one to compute the surface critical exponent in one dimension analytically. Moreover, we discuss the mean field limit that is expected to be valid in d>4 space dimensions and demonstrate how the corresponding partial differential equations can be solved.Comment: 8 pages, 4 figures; v1 was changed by replacing the co-authors name "L\"ubeck" with "Lubeck" (metadata only

Finite-size scaling of directed percolation in the steady state

Recently, considerable progress has been made in understanding finite-size scaling in equilibrium systems. Here, we study finite-size scaling in non-equilibrium systems at the instance of directed percolation (DP), which has become the paradigm of non-equilibrium phase transitions into absorbing states, above, at and below the upper critical dimension. We investigate the finite-size scaling behavior of DP analytically and numerically by considering its steady state generated by a homogeneous constant external source on a d-dimensional hypercube of finite edge length L with periodic boundary conditions near the bulk critical point. In particular, we study the order parameter and its higher moments using renormalized field theory. We derive finite-size scaling forms of the moments in a one-loop calculation. Moreover, we introduce and calculate a ratio of the order parameter moments that plays a similar role in the analysis of finite size scaling in absorbing nonequilibrium processes as the famous Binder cumulant in equilibrium systems and that, in particular, provides a new signature of the DP universality class. To complement our analytical work, we perform Monte Carlo simulations which confirm our analytical results.Comment: 21 pages, 6 figure

Universal scaling behavior of non-equilibrium phase transitions

One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to a given universality class have the same critical exponents, and certain scaling functions become identical near the critical point. It is the aim of this work to demonstrate the usefulness of universal scaling functions for the analysis of non-equilibrium phase transitions. In order to limit the coverage of this article, we focus on a particular class of non-equilibrium critical phenomena, the so-called absorbing phase transitions. These phase transitions arise from a competition of opposing processes, usually creation and annihilation processes. The transition point separates an active phase and an absorbing phase in which the dynamics is frozen. A systematic analysis of universal scaling functions of absorbing phase transitions is presented, including static, dynamical, and finite-size scaling measurements. As a result a picture gallery of universal scaling functions is presented which allows to identify and to distinguish universality classes.Comment: review article, 160 pages, 60 figures include

La législation de la Houille Blanche en Suède

Sven-Lübeck . La législation de la Houille Blanche en Suède. In: Deuxième congrès de la Houille blanche, Lyon, septembre 1914. Rapports qui devaient être présentés au congrès. Tome 1, 1914

Non-equilibrium phase transitions

This book describes two main classes of non-equilibrium phase-transitions: (a) static and dynamics of transitions into an absorbing state, and (b) dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. The first volume begins with an introductory chapter which recalls the main concepts of phase-transitions, set for the convenience of the reader in an equilibrium context. The extension to non-equilibrium systems is made by using directed percolation as the main paradigm of absorbing phase transitions and in view of the richness of the known results an entire chapter is devoted to it, including a discussion of recent experimental results. Scaling theories and a large set of both numerical and analytical methods for the study of non-equilibrium phase transitions are thoroughly discussed. The techniques used for directed percolation are then extended to other universality classes and many important results on model parameters are provided for easy reference.This book is Volume 2 of a two-volume set describing two main classes of non-equilibrium phase-transitions. This volume covers dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. Motivated initially by experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding of far from equilibrium relaxation. Dynamical scaling is systematically introduced, starting from coarsening phenomena, and existing analytical results and numerical estimates of universal non-equilibrium exponents and scaling functions are reviewed in detail. Ageing phenomena in glasses, as well as in simple magnets, are paradigmatic examples of non-equilibrium dynamical scaling, but may also be found in irreversible systems of chemical reactions. Recent theoretical work sought to understand if dynamical scaling may be just a part of a larger symmetry, called local scale-invariance. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions; this work has recently reached a degree of completion and the research is presented, systematically and in detail, in book form for the first time. Numerous worked-out exercises are included. Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points

Universal scaling behavior of non-equilibrium phase transitions

Non-equilibrium critical phenomena have attracted a lot of research interest in the recent decades. Similar to equilibrium critical phenomena, the concept of universality remains the major tool to order the great variety of non-equilibrium phase transitions systematically. All systems belonging to a given universality class share the same set of critical exponents, and certain scaling functions become identical near the critical point. It is known that the scaling functions vary more widely between different uni-versality classes than the exponents. Thus, universal scaling functions offer a sensitive and accurate test for a system’s universality class. On the other hand, universal scaling functions demonstrate the robustness of a given universality class impressively. Unfor-tunately, most studies focus on the determination of the critical exponents, neglecting the universal scaling functions. In this work a particular class of non-equilibrium critical phenomena is considered, the so-called absorbing phase transitions. Absorbing phase transitions are expected to occur in physical, chemical as well as biological systems, and a detailed introduc-tion is presented. The universal scaling behavior of two different universality classes i

Professionalisierung durch Fallarbeit für die inklusive Schule

Heinrich M, Blasse N, Budde J, et al. Professionalisierung durch Fallarbeit für die inklusive Schule. In: Ricken G, Degenhardt S, eds. Vernetzung, Kooperation, Sozialer Raum. Inklusion als Querschnittaufgabe. Perspektiven sonderpädagogischer Forschung . Bad Heilbrunn: Julius Klinkhardt; 2019: 159-181