STUDY OF FINITE SIZE EFFECTS ON DIRECTED SPIRAL PERCOLATION

2003 ◽  
Vol 17 (29) ◽  
pp. 5555-5564 ◽  
Author(s):  
S. B. SANTRA
Keyword(s):  
Finite Size ◽  
System Size ◽  
Square Lattice ◽  
Finite Size Effects ◽  
Infinite Cluster ◽  
Percolation Clusters ◽  
Large Lattice ◽  
Infinite Network ◽  
Large Systems ◽  
Good Agreement

Percolation under both directional and rotational constraints is studied numerically on the square lattice of different finite sizes L. The critical percolation threshold pc≈0.655 of the infinite network is determined by extrapolating the finite size data. The fractal dimension df of the infinite percolation clusters is found df≈1.72 from the finite size scaling, S∞~Ldf where S∞ is the mass of the infinite cluster. The critical exponents are estimated as a function of the system size L. It is seen that the results of smaller systems converge to that of the large systems. The results are then extrapolated to the infinite network. The extrapolated results for the infinite network are compared with Monte Carlo results on a single large lattice. A good agreement is found.

a0(980) AND f0(980) MESONS AS HADRONIC MOLECULES

2009 ◽  
Vol 24 (02n03) ◽  
pp. 568-571 ◽  
Author(s):  
T. BRANZ ◽  
T. GUTSCHE ◽  
V. E. LYUBOVUTSKIJ
Keyword(s):  
Size Effects ◽  
Bound States ◽  
Finite Size ◽  
Finite Size Effects ◽  
Gauge Invariant ◽  
Electromagnetic Decay ◽  
Invariant Model ◽  
Scalar Mesons ◽  
Decay Properties ◽  
Good Agreement

We discuss a possible interpretation of the scalar mesons f0(980) and a0(980) as hadronic molecules - bound states of K and [Formula: see text] mesons. Using a phenomenological Lagrangian approach we calculate strong as well as the electromagnetic decay properties of both scalars. The covariant and gauge invariant model, which also allows for finite size effects of the hadronic molecule, delivers results in good agreement with experimental data.

SCALING AND FINITE-SIZE EFFECTS FOR THE CRITICAL BACKBONE

Fractals ◽  
2003 ◽  
Vol 11 (supp01) ◽  
pp. 19-27 ◽  
Author(s):  
M. BARTHELEMY ◽  
S. V. BULDYREV ◽  
S. HAVLIN ◽  
H. E. STANLEY
Keyword(s):  
Fractal Dimension ◽  
Probability Distribution ◽  
Size Effects ◽  
Infinite System ◽  
Finite Size ◽  
Multifractal Spectrum ◽  
System Size ◽  
Two Dimensional ◽  
High Current ◽  
Finite Size Effects

In a first part, we study the backbone connecting two given sites of a two-dimensional lattice separated by an arbitrary distance r in a system of size L. We find a scaling form for the average backbone mass and we also propose a scaling form for the probability distribution P(MB) of backbone mass for a given r. For r ≈ L, P(MB) is peaked around LdB, whereas for r ≪ L, P(MB) decreases as a power law, [Formula: see text], with τB ≃ 1.20 ± 0.03. The exponents ψ and τB satisfy the relation ψ = dB(τB - 1), and ψ is the codimension of the backbone, ψ = d - dB. In a second part, we study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small i as P(i) ~ 1/i where i is the current. As a consequence, the moments of i of order q ≤ qc = 0 diverge with system size, and all sets of bonds with current values below the most probable one have the fractal dimension of the backbone. Hence we hypothesize that the backbone can be described in terms of only (i) blobs of fractal dimension dB and (ii) high current carrying bonds of fractal dimension going from d red to dB, where d red is the fractal dimension of the red bonds carrying the maximal current.

CROSSOVER TO GAUSSIAN BEHAVIOR IN HERDING MARKET MODELS

2001 ◽  
Vol 12 (08) ◽  
pp. 1211-1215 ◽  
Author(s):  
L. KULLMANN ◽  
J. KERTÉSZ
Keyword(s):  
Size Effects ◽  
Size Dependence ◽  
Finite Size ◽  
Finite Size Effects ◽  
Market Models ◽  
Number Of Clusters ◽  
Percolation Clusters ◽  
Cluster Distribution ◽  
Spatial Dimensions ◽  
One Step

We have analyzed possible mechanisms of the crossover to the Gaussian distribution of the logarithmic returns in the Cont–Bouchaud herding model of the stock market. Either the underlying cluster distribution is not in the Lévy attraction regime, or a cut-off effect is responsible for the crossover. The cut-off can be due to the finite size of the system, where clusters are created. If such finite size effects are responsible for the crossover, a delicate interplay between the size dependence of the deviation from the Gaussian and of the number of values to be summed up in one step may result in a size-independent crossover value of the activity. It is shown that this is the case for percolation clusters in spatial dimensions from 2 to 6. A further origin of the cut-off can be the limited number of clusters taken into account.

scholarly journals Finite-size effects in parametric subharmonic instability

2014 ◽  
Vol 759 ◽  
pp. 739-750 ◽  
Author(s):  
Baptiste Bourget ◽  
Hélène Scolan ◽  
Thierry Dauxois ◽  
Michael Le Bars ◽  
Philippe Odier ◽  
...  
Keyword(s):  
Size Effects ◽  
Wave Beam ◽  
Finite Size ◽  
Numerical Results ◽  
Finite Width ◽  
Interaction Zone ◽  
Finite Size Effects ◽  
Energy Transfers ◽  
Parametric Subharmonic Instability ◽  
Good Agreement

AbstractThe parametric subharmonic instability (PSI) in stratified fluids depends on the frequency and the amplitude of the primary plane wave. In this paper, we present experimental and numerical results emphasizing that the finite width of the beam also plays an important role on this triadic instability. A new theoretical approach based on a simple energy balance is developed and compared with numerical and experimental results. Owing to the finite width of the primary wave beam, the secondary pair of waves can leave the interaction zone which affects the transfer of energy. Experimental and numerical results are in good agreement with the prediction of this theory, which brings new insights on energy transfers in the ocean where internal waves with finite-width beams are dominant.

scholarly journals Patterns and Long Range Correlations in Idealized Granular Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 953-965 ◽  
Author(s):  
J. A. G. Orza ◽  
R. Brito ◽  
T. P. C. van Noije ◽  
M. H. Ernst
Keyword(s):  
Long Range ◽  
Size Effects ◽  
Hard Spheres ◽  
Finite Size ◽  
System Size ◽  
Spatial Correlations ◽  
Finite Size Effects ◽  
Long Range Correlations ◽  
Intrinsic Length ◽  
Dynamics Simulations

An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field u(r, t) (vortices) and in the density field n (r, t)(clusters), driven by unstable fluctuations, δa = {δn, δu}. Their spatial correlations, <δa(r, t)δa(r′,t)>, as measured in molecular dynamics simulations, exhibit long range correlations; the mean vortex diameter grows as [Formula: see text]; there occur transitions to macroscopic shearing states, etc. The Cahn–Hilliard theory of spinodal decomposition offers a qualitative understanding and quantitative estimates of the observed phenomena. When intrinsic length scales are of the order of the system size, effects of physical boundaries and periodic boundaries (finite size effects in simulations) are important.

scholarly journals Beyond the thermodynamic limit: finite-size corrections to state interconversion rates

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 108 ◽  
Author(s):  
Christopher T. Chubb ◽  
Marco Tomamichel ◽  
Kamil Korzekwa
Keyword(s):  
Thermodynamic Limit ◽  
Size Effects ◽  
Heat Engine ◽  
Finite Size ◽  
Average Energy ◽  
System Size ◽  
Mathematical Framework ◽  
Single Shot ◽  
Final State ◽  
Finite Size Effects

Thermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transformations of finite-size systems. More formally, we analyse state interconversion under thermal operations and between arbitrary energy-incoherent states. We find precise relations between the optimal rate at which interconversion can take place and the desired infidelity of the final state when the system size is sufficiently large. These so-called second-order asymptotics provide a bridge between the extreme cases of single-shot thermodynamics and the asymptotic limit of infinitely large systems. We illustrate the utility of our results with several examples. We first show how thermodynamic cycles are affected by irreversibility due to finite-size effects. We then provide a precise expression for the gap between the distillable work and work of formation that opens away from the thermodynamic limit. Finally, we explain how the performance of a heat engine gets affected when one of the heat baths it operates between is finite. We find that while perfect work cannot generally be extracted at Carnot efficiency, there are conditions under which these finite-size effects vanish. In deriving our results we also clarify relations between different notions of approximate majorisation.

scholarly journals Finite-Size Effects in Stochastic Models of Population Dynamics: Applications to Biomedicine and Biology

2010 ◽  
Author(s):  
Francesca Di Patti
Keyword(s):  
Population Dynamics ◽  
Size Effects ◽  
Life Science ◽  
Finite Size ◽  
System Size ◽  
Microscopic Level ◽  
Finite Size Effects ◽  
Biological Phenomena ◽  
Macroscopic Approach ◽  
System Size Expansion

Population dynamics constitutes a widespread branch of investigations which finds important applications within the realm of life science. The classical deterministic (macroscopic) approach aims at characterizing the time evolution of families of homologous entities, so to unravel the global mechanisms which drive their dynamics. As opposed to this formulation, a microscopic level of modeling can be invoked which instead focuses on the explicit rules governing the interactions among individuals. A viable tool that enables to bridge the gap between the two approaches is the van Kampen's system size expansion. In this thesis we use this method to show how the finite-size effects accounted by the microscopic level might significantly alter the dynamics of biological phenomena.

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