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Gunnar Pruessner

Publications and source records attributed to Gunnar Pruessner.

At least 73 records · Page 4Linked to original sources
arXiv2012

Universality and a numerical ε-expansion of the Abelian Manna model below upper critical dimension

The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration and area distribution of the model are obtained by using a high-accuracy moment analysis. Together with earlier results on lower-dimensional lattices, the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the the coefficients of an ε-expansion. Rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension, a remarkable relation is observed, satisfied by both regular and fractal lattices.

cond-mat.stat-mech↗
arXiv2012

Mounding in Epitaxial Surface Growth

For the past two decades the Villain-Lai-Das Sarma equation has served as the theoretical framework for conserved surface growth processes, such as molecular-beam epitaxy. However some phenomena, such as mounding, are yet to be fully understood. In the following, we present a systematic analysis of the full, original Villain-Lai-Das Sarma equation showing that mound forming terms, which should have been included initially on symmetry grounds, are generated under renormalisation. A number of widely studied Langevin equations are recovered as limits or trivial fixed points of the full theory.

cond-mat.stat-mech↗
arXiv2011

Abelian Manna model on various lattices in one and two dimensions

We perform a high-accuracy moment analysis of the avalanche size, duration and area distribution of the Abelian Manna model on eight two-dimensional and four one-dimensional lattices. The results provide strong support to establish universality of exponents and moment ratios across different lattices and a good survey for the strength of corrections to scaling which are notorious in the Manna universality class. The results are compared against previous work done on Manna model, Oslo model and directed percolation. We also confirm hypothesis of various scaling relations.

cond-mat.stat-mech↗
arXiv2010

The Edwards-Wilkinson equation with drift and Neumann boundary conditions

The well known scaling of the Edwards-Wilkinson equation is essentially determined by dimensional analysis. Once a drift term is added, more sophisticated reasoning is required, which initially suggests that the drift term dominates over the diffusion. However, the diffusion term is dangerously irrelevant and the resulting scaling in fact non-trivial. In the present article we compare the resulting scaling of the Edwards-Wilkinson equation with drift and Neumann boundary conditions to the published case with Dirichlet boundary conditions.

cond-mat.stat-mech↗
arXiv2010

The Abelian Manna model on two fractal lattices

We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension d_g=ln(3)/ln(2), with the aim to probe for scaling behavior and to study the systematic dependence of the critical exponents on the dimension and structure of the lattices. We show that the scaling law D(2-tau)=d_w generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where d_w=2. Furthermore, we observe that the lattice dimension d_g, the fractal dimension of the random walk on the lattice d_w, and the critical exponent D, form a plane in 3D parameter space, i.e. they obey the linear relationship D=0.632(3) d_g + 0.98(1) d_w - 0.49(3).

cond-mat.stat-mech↗
arXiv2009

Tuning- and order parameter in the SOC ensemble

The one-dimensional Oslo model is studied under self-organized criticality (SOC) conditions and under absorbing state (AS) conditions. While the activity signals the phase transition under AS conditions by a sudden increase, this is not the case under SOC conditions. The scaling parameters of the activity are found to be identical under SOC and AS conditions, but in SOC the activity lacks a pickup.

cond-mat.stat-mech↗
arXiv2008

Block scaling in the directed percolation universality class

The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its fluctuations, considering (sub-)blocks of linear size l in systems of linear size L. The scaling depends on the choice of the ensemble, as only the conditional ensemble produces the block-scaling behaviour as established in equilibrium critical phenomena. The dependence on the ensemble can be understood by an additional symmetry present in the unconditional ensemble. The unconventional scaling found in the unconditional ensemble is a reminder of the possibility that scaling functions themselves have a power-law dependence on their arguments.

cond-mat.stat-mech↗
arXiv2008

Reply to "Comment on `Self-organized Criticality and Absorbing States: Lessons from the Ising Model'"

In [Braz. J. Phys. 30, 27 (2000)] Dickman et al. suggested that self-organized criticality can be produced by coupling the activity of an absorbing state model to a dissipation mechanism and adding an external drive. We analyzed the proposed mechanism in [Phys. Rev. E 73, 025106R (2006)] and found that if this mechanism is at work, the finite-size scaling found in self-organized criticality will depend on the details of the implementation of dissipation and driving. In the preceding comment [Phys. Rev. E XX, XXXX (2008)] Alava et al. show that one avalanche exponent in the AS approach becomes independent of dissipation and driving. In our reply we clarify their findings and put them in the context of the original article.

cond-mat.stat-mech↗
arXiv2008

On the scaling of probability density functions with apparent power-law exponents less than unity

We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent \tautilde of a probability density is less than 1, the associated finite-size scaling ansatz has a scaling exponent τequal to 1, provided that the fraction of events in the universal scaling part of the probability density function is non-vanishing in the thermodynamic limit. We find the general result that τ>=1 and τ>=\tautilde. Moreover, we show that if the scaling function G(x) approaches a non-zero constant for small arguments, \lim_{x-> 0} G(x) > 0, then τ=\tautilde. However, if the scaling function vanishes for small arguments, \lim_{x-> 0} G(x) = 0, then τ=1, again assuming a non-vanishing fraction of universal events. Finally, we apply the formalism developed to examples from the literature, including some where misunderstandings of the theory of scaling have led to erroneous conclusions.

cond-mat.stat-mech↗
arXiv2007

Equivalence of conditional and external field ensembles in absorbing state phase transitions

I comment on the relation between two sampling methods for absorbing state models. It is shown that a certain ensemble without external field conditional to activity coincides with the unconditional ensemble for sufficiently small external field. The actual physical processes involved are identical and the derivation of the identity of the scaling behaviour relies on a single (established) scaling law. While the conditional ensemble by construction does not contain information about the system with large external field, it contains all information about the limit of vanishing external field and about the vicinity of the critical point: Finite size scaling as well as critical scaling in the temperature-like variable or in (small) external field.

cond-mat.stat-mech↗
arXiv2007

Phase field model of interfaces in single-component systems derived from classical density functional theory

Phase field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived from first principles. In single-component systems the free energy is a functional of a ``phase field'', which is an order parameter often referred to as the crystallinity in the context of grain boundaries, but with no precise definition as to what that term means physically. We present a derivation of the phase field model by Allen and Cahn from classical density functional theory first for crystal-liquid interfaces and then for grain boundaries. The derivation provides a clear physical interpretation of the phase field, and it sheds light on the parameters and the underlying approximations and limitations of the theory. We suggest how phase field models may be improved.

cond-mat.mtrl-sci↗
arXiv2007

Multiscaling in the sequence of areas enclosed by coalescing random walkers

We address the question whether the sequence of areas between coalescing random walkers displays multiscaling and in the process calculate the second moment as well as the two point correlation function exactly. The scaling of higher order correlation functions is estimated numerically, indicating a logarithmic dependence on the system size. Together with the analytical results, this confirms the presence of multiscaling.

cond-mat.stat-mech↗
arXiv2006

Strongly anisotropic roughness in surfaces driven by an oblique particle flux

Using field theoretic renormalization, an MBE-type growth process with an obliquely incident influx of atoms is examined. The projection of the beam on the substrate plane selects a "parallel" direction, with rotational invariance restricted to the transverse directions. Depending on the behavior of an effective anisotropic surface tension, a line of second order transitions is identified, as well as a line of potentially first order transitions, joined by a multicritical point. Near the second order transitions and the multicritical point, the surface roughness is strongly anisotropic. Four different roughness exponents are introduced and computed, describing the surface in different directions, in real or momentum space. The results presented challenge an earlier study of the multicritical point.

cond-mat.stat-mech↗
arXiv2006

Novel surface universality classes with strong anisotropy

Using renormalized field theory, we examine the dynamics of a growing surface, driven by an obliquely incident particle beam. Its projection on the reference (substrate) plane selects a ``parallel'' direction, so that the evolution equation for the surface height becomes anisotropic. The phase diagram of the model is controlled by the properties of an effective anisotropic surface tension. Our renormalization group analysis suggests the existence of a line of continuous transitions and a line of (potentially) first-order transitions, which meet at a multicritical point. The full scaling behavior for the continuous line and the multicritical point is discussed in detail. Two novel universality classes for scale-invariant surface fluctuations are found.

cond-mat.stat-mech↗
arXiv2005

Comment on: "Superscaling of Percolation on Rectangular Domains"

In [Watanabe et al., Phys. Rev. Lett. 93 190601 (2004)], the authors show numerically that spanning and percolation probabilities in two-dimensional systems with different aspect ratios obey a form of "superscaling". In this comment, we would like to point out some difficulties with their proposed scaling ansatz and suggest why this remained undetected in their numerical analysis.

cond-mat.stat-mech↗
arXiv2005

Spurious phase in a model for traffic on a bridge

We present high-precision Monte Carlo data for the phase diagram of a two-species driven diffusive system, reminiscent of traffic across a narrow bridge. Earlier studies reported two phases with broken symmetry; the existence of one of these has been the subject of some debate. We show that the disputed phase disappears for sufficiently large systems and/or sufficiently low bulk mobility.

cond-mat.stat-mech↗
arXiv2005

Orthogonal polynomials with discontinuous weights

In this paper we present a brief description of a ladder operator formalism applied to orthogonal polynomials with discontinuous weights. The two coefficient functions, A_n(z) and B_n(z), appearing in the ladder operators satisfy the two fundamental compatibility conditions previously derived for smooth weights. If the weight is a product of an absolutely continuous reference weight w_0 and a standard jump function, then A_n(z) and B_n(z) have apparent simple poles at these jumps. We exemplify the approach by taking w_0 to be the Hermite weight. For this simpler case we derive, without using the compatibility conditions, a pair of difference equations satisfied by the diagonal and off-diagonal recurrence coefficients for a fixed location of the jump. We also derive a pair of Toda evolution equations for the recurrence coefficients which, when combined with the difference equations, yields a particular Painleve IV.

math-ph↗