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1.
Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated in this model are generally rarefied and have chiral dangling ends on both the square and triangular lattices. It is found that the clusters are more compact and less anisotropic on the triangular lattice than on the square lattice. The elongation of the clusters is in a different direction than the imposed directional constraint on both the lattices. The values of some of the critical exponents and fractal dimension are found considerably different on the two lattices. The DSP model then exhibits a breakdown of universality in 2D between the square and triangular lattices. The values of the critical exponents obtained for the triangular lattice are not only different from that of the square lattice but also different form other percolation models.Received: 12 March 2004, Published online: 23 July 2004PACS:
02.50.-r Probability theory, stochastic processes, and statistics - 64.60.-i General studies of phase transitions - 72.80.Tm Composite materials 相似文献
2.
M.L. Ndawana R.A. Römer M. Schreiber 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(3):399-407
We compute the number level variance Σ
2 and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be
used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With
N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level
spacing, we find that both χ(N, W) and the integrated Σ
2 obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder
given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W
c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06
at the metal-insulator transition in very close agreement with previous results.
Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002 相似文献
3.
H. J. Herrmann 《Zeitschrift für Physik B Condensed Matter》1979,32(3):335-337
Analysis of Monte Carlo data shows the density profiles of critical percolation clusters (p=p
c
) to be similar to each other. The same is true for random animals (p=0). The exponents for these scaling laws are determined and agree with those expected from the cluster radii. 相似文献
4.
We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant
force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of
the polymers N is varied in the range 8 < N < 128, and the obstacle concentration in the medium C is varied from zero up to the percolation threshold C≈ 0.75. For field intensities below a C-dependent critical field strength B
c, where jamming effects become dominant, we find that the conformational properties of the drifting chains can be interpreted
as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity
B
c itself is found to decrease linearly with C.
Received 20 August 2001 and Received in final form 19 November 2001 相似文献
5.
L. Turban 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(3):331-338
Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation
threshold. In a dynamical interpretation, the crossing probability is the probability that, on a system with size L, an epidemic spreading without immunization remains active at time t. Since the system is strongly anisotropic, the shape dependence in space-time enters through the effective aspect ratio r
eff = ct/L
z, where c is a non-universal constant and z the anisotropy exponent. A particular attention is paid to the influence of the initial state on the universal behaviour
of the crossing probability. Using anisotropic finite-size scaling and generalizing a simple argument given by Aizenman for
isotropic percolation, we also obtain the behaviour of the probability to find n incipient spanning clusters on a finite system at time t. The numerical results are in good agreement with the conjecture.
Received 10 February 2003 Published online 20 June 2003
RID="a"
ID="a"e-mail: turban@lpm.u-nancy.fr
RID="b"
ID="b"UMR CNRS 7556 相似文献
6.
Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation
rules are a combination of probabilistic critical height (probability of toppling p) and deterministic critical slope processes with internal correlation time tc equal to the avalanche lifetime, in model A, and ,in model B. In both cases nonuniversal scaling properties of avalanche distributions are found for , where is related to directed percolation threshold in d=3. Distributions of avalanche durations for are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B,
and scaling exponents are determined as a function of p. At a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics
at approaches the parity conserving universality class in model A, and the mean-field universality class in model B. We also
estimate roughness exponent at the transition.
Received: 29 May 1998 / Revised: 8 September 1998 / Accepted: 10 September 1998 相似文献
7.
D.L. Peng T.J. Konno K. Wakoh T. Hihara K. Sumiyama 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,16(1):329-332
Cluster-cluster coalescence process of monodispersed Co clusters with mean diameter d = 8.5 and 13 nm deposited a plasma-gas-condensation-type cluster beam deposition system was investigated by in situ electrical conductivity measurements and ex situ scanning electron microscopy (SEM) and transmission electron microscopy (TEM), and analyzed by percolation concept. The electrical
conductivity measurement and TEM observation indicated that, below temperature T≈ 100°C, the Co clusters in the assemblies maintain their original structure as deposited at room temperature, while that the inter-cluster
coalescence takes place at T > 100°C, although the size distribution and the interface morphology of the clusters showed no marked change at substrate temperatures
T
s≤200°C.
Received 29 November 2000 相似文献
8.
H. Chamati D.M. Dantchev 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(1):89-99
The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite
O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic
boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r
- (d + σ), where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs
to the short-range universality class it is shown that above the bulk critical temperature T
c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems.
Received 8 August 2001 相似文献
9.
A nanosecond scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as
it nears the glass transition. The scaling behaviour is in the same universality class as percolation. The exponents γ and
β are found to be 1.7±0.1 and 0.41±0.01 in agreement with the best percolation results in three dimensions.
Received 29 August 2002
RID="a"
ID="a"e-mail: erzan@gursey.gov.tr e-mail: erzan@itu.edu.tr 相似文献
10.
J.E. Santos U.C. Täuber 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(4):423-440
Second-order phase transitions in a non-equilibrium liquid-gas model with reversible mode couplings, i.e., model H for binary-fluid critical dynamics, are studied using dynamic field theory and the renormalization group. The system
is driven out of equilibrium either by considering different values for the noise strengths in the Langevin equations describing
the evolution of the dynamic variables (effectively placing these at different temperatures), or more generally by allowing
for anisotropic noise strengths, i.e., by constraining the dynamics to be at different temperatures in d
|| - and d
⊥-dimensional subspaces, respectively. In the first, isotropic case, we find one infrared-stable and one unstable renormalization group fixed point. At the stable fixed point, detailed
balance is dynamically restored, with the two noise strengths becoming asymptotically equal. The ensuing critical behavior
is that of the standard equilibrium model H. At the novel unstable fixed point, the temperature ratio for the dynamic variables
is renormalized to infinity, resulting in an effective decoupling between the two modes. We compute the critical exponents
at this new fixed point to one-loop order. For model H with spatially anisotropic noise, we observe a critical softening only in the d
⊥-dimensional sector in wave vector space with lower noise temperature. The ensuing effective two-temperature model H does
not have any stable fixed point in any physical dimension, at least to one-loop order. We obtain formal expressions for the
novel critical exponents in a double expansion about the upper critical dimension d
c = 4 - d
|| and with respect to d
|| , i.e., about the equilibrium theory.
Received 4 April 2002 Published online 13 August 2002 相似文献
11.
S. Sinha S. B. Santra 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(3):429-435
Unbiased random walks are performed on topologically biased anisotropic percolation clusters (APC). Topologically biased APCs
are generated using suitable anisotropic percolation models. New walk dimensions are found to characterize the anisotropic
behaviour of the unbiased random walk on the biased topology. Critical properties of electro and magneto conductivities are
characterized estimating respective dynamical critical exponents. A dynamical scaling theory relating dynamical and static
critical exponents has been developed. The dynamical critical exponents satisfy the scaling relations within error bar. 相似文献
12.
G. Migliorini V.G. Rostiashvili T.A. Vilgis 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(1):61-73
The Langevin dynamics of a self-interacting chain embedded in a quenched random medium is investigated by making use of the
generating functional method and one-loop (Hartree) approximation. We have shown how this intrinsic disorder causes different
dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding
subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval
the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, (Δ/b
d)N
2 - νd≥1, where Δ is a disorder strength, b is a Kuhnian segment length, N is a chain length and ν is the Flory exponent. We have derived the general equation for the non-ergodicity function f (p) which characterizes the amplitude of frozen Rouse modes with an index p = 2πj/N. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same
critical disorder strength Δ
c ∼ N
- γ where the exponent γ ≈ 0.25 and does not depend from the solvent quality.
Received 17 December 2002 Published online 23 May 2003
RID="a"
ID="a"e-mail: vilgis@mpip-mainz.mpg.de 相似文献
13.
M. Hiane J. Ebothé 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,22(4):485-495
We show that the electrodeposition of Ni-Zn alloys at the lowest growth velocities, v < 0.5μm/s, exclusively proceeds from an abnormal co-deposition phenomenon. The growth process in this v region greatly depends on the initial [Co2+] concentration of the film deposition bath. A theoretical approach of this process including the role of the saturation surface
roughness of the alloy, , leads to an estimation of the transport properties of the ad-atoms involved during the deposit formation. Their surface
diffusion coefficient varying between 1.76×10-10 and 2.40×10-8 cm-2/s exhibits a minimal value, D
s = 2.10×10-10 cm-2/s located between v = 0.17 and 0.35μm/s. The spatial scaling analysis of the local roughness, σ, examined according to the power-law σ≈L
α reveals that the resulting roughness exponents concurs with the Kardar-Parisi-Zhang dynamics including the restricted surface
diffusion. Two main v regions leads to different fractal textural features of the alloy film surface. Below 0.10 μm/s, the roughness exponent obtained
is α≈ 0.6, depicting a limited ad-atom mobility. Over v = 0.30μm/s, this exponent stabilises at α≈ 0.82, indicating an increase of the surface diffusion.
Received 16 August 2000 and Received in final form 20 June 2001 相似文献
14.
15.
Deepak Dhar 《Pramana》2002,58(2):419-426
This article reviews some effects of disorder in percolation systems away from the critical density p
c. For densities below p
c, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee-Yang
edge singularity problem is described. Rare compact clusters give rise to Griffiths singularities in the free energy of diluted
ferromagnets, and lead to a very slow relaxation of magnetization. In biased diffusion on percolation clusters, trapping in
dead-end branches leads to asymptotic drift velocity becoming zero for strong bias, and very slow relaxation of velocity near
the critical bias field. 相似文献
16.
B. Mazzi F. Okkels J.C. Vassilicos 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(2):243-251
We present a shell-model of fractal induced turbulence which predicts that structure function scaling exponents decrease in
absolute value as the fractal dimension of the turbulence-inducing fractal object increases. This qualitative prediction is
in agreement with laboratory measurements. Finer details of the fractal induced turbulence statistics and dynamics depend
on the fractal force's phases, i.e. on the detailed construction of the fractal stirrer. In a case of deterministic forcing phases, a critical fractal dimension
exists below which the average rate of inter-scale energy transfer <T
n> is a decreasing function of the wavenumber kn and the structure function scaling exponents take close to Kolmogorov values. Above this critical fractal dimension, <T
n> is an increasing function of kn and the structure function scaling exponents deviate significantly from Kolmogorov values.
Received 25 June 2001 / Received in final form 5 April 2002 Published online 19 July 2002 相似文献
17.
Y. Y. Tarasevich V. A. Cherkasova 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(1):97-100
We consider site percolation of dimers (“needles”) on simple cubic lattice. The percolation threshold is estimated as pc
perc ≈ 0.2555 ± 0.0001. The jamming threshold is estimated as pc
jamm = 0.799 ± 0.002. 相似文献
18.
Hans-Karl Janssen 《Annals of Physics》2005,315(1):147-192
We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic features are governed, respectively, by the directed (DP) and dynamic isotropic percolation (dIP) universality classes. We discuss the construction of a field theory representation for these Markovian stochastic processes based on fundamental phenomenological considerations, as well as from a specific microscopic reaction-diffusion model realization. Subsequently we explain how dynamic renormalization group (RG) methods can be applied to obtain the universal properties near the critical point in an expansion about the upper critical dimensions dc = 4 (DP) and 6 (dIP). We provide a detailed overview of results for critical exponents, scaling functions, crossover phenomena, finite-size scaling, and also briefly comment on the influence of long-range spreading, the presence of a boundary, multispecies generalizations, coupling of the order parameter to other conserved modes, and quenched disorder. 相似文献
19.
M. C. T. P. Carvalho J. A. M. S. Duarte 《Zeitschrift für Physik B Condensed Matter》1988,70(2):203-208
Exact series for lattices of dimension between 2 and 6 are used to report on the asymptotic features of the scaling function for the average number of clusters in directed percolation, close to, and away from, the most recent estimated intervals forp
c
. Scanning of the noncritical regions yields exponent ranges compatible with the undirected percolation equivalents. Close top
c
the scaling function varies fairly linearly in terms of the variablez=(p–p
c
)s
and this result is rather stable particularly bearing in mind the modestly available precision forp
c
in higher dimensionalities. 相似文献
20.
M. Bauer O. Golinelli 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,24(3):339-352
We study both numerically and analytically what happens to a random graph of average connectivity α when its leaves and their
neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated vertices plus an induced
subgraph we call the core. In the thermodynamic limit of an infinite random graph, we compute analytically the dynamics of leaf removal, the number
of isolated vertices and the number of vertices and edges in the core. We show that a second order phase transition occurs
at α = e = 2.718 ... : below the transition, the core is small but above the transition, it occupies a finite fraction of
the initial graph. The finite size scaling properties are then studied numerically in detail in the critical region, and we
propose a consistent set of critical exponents, which does not coincide with the set of standard percolation exponents for
this model. We clarify several aspects in combinatorial optimization and spectral properties of the adjacency matrix of random
graphs.
Received 31 January 2001 and Received in final form 26 June 2001 相似文献