Scaling behavior of granular particles in a vibrating box

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

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Scaling behavior of discretization errors in renormalization and improvement constants

Physical Review D ◽

10.1103/physrevd.73.114507 ◽

2006 ◽

Vol 73 (11) ◽

Cited By ~ 5

Author(s):

Tanmoy Bhattacharya ◽

Rajan Gupta ◽

Weonjong Lee ◽

Stephen R. Sharpe

Keyword(s):

Scaling Behavior ◽

Discretization Errors

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Disorientations in dislocation structures: Formation and spatial correlation

Journal of Materials Research ◽

10.1557/jmr.2002.0355 ◽

2002 ◽

Vol 17 (9) ◽

pp. 2433-2441 ◽

Cited By ~ 17

Author(s):

Wolfgang Pantleon

Keyword(s):

Plastic Deformation ◽

Spatial Correlation ◽

Distribution Functions ◽

Scaling Behavior ◽

Dislocation Dynamics ◽

Slip Systems ◽

Experimental Findings ◽

Good Agreement

During plastic deformation, dislocation boundaries are formed and orientation differences across them arise. Two different causes lead to the formation of two kinds of deformation-induced boundaries: a statistical trapping of dislocations in incidental dislocation boundaries and a difference in the activation of slip systems on both sides of geometrically necessary boundaries. On the basis of these mechanisms, the occurrence of disorientations across both types of dislocation boundaries is modeled by dislocation dynamics. The resulting evolution of the disorientation angles with strain is in good agreement with experimental observations. The theoretically obtained distribution functions for the disorientation angles describe the experimental findings well and explain their scaling behavior. The model also predicts correlations between disorientations in neighboring boundaries, and evidence for their existence is presented.

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SCALING BEHAVIOR OF THE DENDRITIC BRANCHES OF THALAMIC NEURONS

Fractals ◽

10.1142/s0218348x93000186 ◽

1993 ◽

Vol 01 (02) ◽

pp. 171-178 ◽

Cited By ~ 10

Author(s):

KLAUS-D. KNIFFKI ◽

MATTHIAS PAWLAK ◽

CHRISTIANE VAHLE-HINZ

Keyword(s):

Growth Process ◽

Scaling Law ◽

Branching Ratio ◽

Scaling Behavior ◽

Neuronal Growth ◽

Thalamic Neurons ◽

Dendritic Trees ◽

Ventrobasal Complex ◽

Dendritic Branches

The morphology of Golgi-impregnated thalamic neurons was investigated quantitatively. In particular, it was sought to test whether the dendritic bifurcations can be described by the scaling law (d0)n=(d1)n+(d2)nwith a single value of the diameter exponent n. Here d0 is the diameter of the parent branch, d1 and d2 are the diameters of the two daughter branches. Neurons from two functionally distinct regions were compared: the somatosensory ventrobasal complex (VB) and its nociceptive ventral periphery (VBvp). It is shown that for the neuronal trees studied in both regions, the scaling law was fulfilled. The diameter exponent n, however, was not a constant. It increased from n=1.76 for the 1st order branches to n=3.92 for the 7th order branches of neurons from both regions. These findings suggest that more than one simple intrinsic rule is involved in the neuronal growth process, and it is assumed that the branching ratio d0/d1 is not required to be encoded genetically. Furthermore, the results support the concept of the dendritic trees having a statistically identical topology in neurons of VB and VBvp and thus may be regarded as integrative modules.

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