ANOMALOUS INTERFACE ROUGHENING: THE ROLE OF A GRADIENT IN THE DENSITY OF PINNING SITES

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 818-826 ◽  
Author(s):  
L.A.N. AMARAL ◽  
A.-L. BARABÁSI ◽  
S.V. BULDYREV ◽  
S. HAVLIN ◽  
H.E. STANLEY
Keyword(s):  
Correlation Length ◽  
Qualitative Agreement ◽  
Critical Concentration ◽  
Scaling Properties ◽  
Correlation Lengths ◽  
Longitudinal Correlation ◽  
New Correlation ◽  
Roughness Exponent ◽  
Interface Roughening

We study the effect on interface roughening of a gradient ∇p in the density of pinning sites p. We identify a new correlation length, ξ, which is a function of ∇p: ξ~(∇p)−γ/α, where α=ν⊥/ν|| is the roughness exponent, and γ=ν⊥/(1+ν⊥). The exponents ν⊥ and ν|| characterize the transverse and longitudinal correlation lengths. To investigate the effect of ∇p on the scaling properties of the interface in (1+1) and (2+1) dimensions, we calculate the critical concentration, pc, and the exponents γ and α from which ν⊥ and ν|| can be determined. Our results are in qualitative agreement with some of the features of imbibition experiments.

scholarly journals Topographic Analysis of Wetlandscapes: Fractal Dimension and Scaling Properties

10.29007/c7r5 ◽  
2018 ◽  
Author(s):  
Leonardo Enrico Bertassello ◽  
P. Suresh Rao ◽  
Gianluca Botter ◽  
Antoine Aubeneau
Keyword(s):  
Fractal Dimension ◽  
The United States ◽  
Self Similarity ◽  
Topographic Analysis ◽  
Scaling Properties ◽  
Dem Analysis ◽  
Water Filling ◽  
Topographic Depressions ◽  
And Storage

Wetlands are ubiquitous topographic depressions on landscapes and form criticalelements of the mosaic of aquatic habitats. The role of wetlands in the global hydrological and biogeochemical cycles is intimately tied to their geometric characteristics. We used DEM analysis and local search algorithms to identify wetland attributes (maximum stage, surface area and storage volume) in four wetlandscapes across the United States. We then derived the exceedance cumulative density functions (cdfs) of these attributes for the identified wetlands, applied the concept of fractal dimension to investigate the variability in wetland’ shapes. Exponentially tempered Pareto distributions were fitted to DEM derived wetland attributes. In particular, the scaling exponents appear to remain constant through the progressive water-filling of the landscapes, suggesting self-similarity of wetland geometrical attributes. This tendency is also reproduced by the fractal dimension (D) of wetland shorelines, which remains constant across different water-filling levels. In addition, the variability in D is constrained within a narrow range (1 <D < 1.33) in all the four wetlandscapes. Finally, the comparison between wetlands identified by the DEM-based model are consistentwith actual data.

Scaling properties of driven interfaces: Symmetries, conservation laws, and the role of constraints

1991 ◽  
Vol 43 (10) ◽  
pp. 5275-5283 ◽  
Author(s):  
Z. Rácz ◽  
M. Siegert ◽  
D. Liu ◽  
M. Plischke
Keyword(s):  
Conservation Laws ◽  
Scaling Properties

Self-affine Fracture Surface Parameters and Their Relationship with Microstructure in a Cast Aluminum Alloy

2002 ◽  
Vol 17 (6) ◽  
pp. 1276-1282 ◽  
Author(s):  
M. Hinojosa ◽  
J. Aldaco
Keyword(s):  
Aluminum Alloy ◽  
Fracture Surface ◽  
The Self ◽  
Cast Aluminum Alloy ◽  
Cast Aluminum ◽  
Force Microscopy ◽  
Fracture Surfaces ◽  
Atomic Force ◽  
Roughness Exponent

The possible role of microstructural features in determining the self-affinity of the fracture surface of a cast aluminum alloy is explored in this work. Fracture surfaces generated both in tension and impact tests were topometrically analyzed by atomic force microscopy, scanning electron microscopy, and stylus profilometry. The roughness exponent exhibited the “universal” value ζ ≈ 0.78, and the correlation length ζ was of the order of the grain size. The brittle intermetallic compounds known to be important in crack initiation did not show any correlation with the self-affine parameters of the resulting fracture surfaces in this particular case.

Structure of Cd-Ga Melts Part 2: X-Ray Small-Angle Scattering

1980 ◽  
Vol 35 (9) ◽  
pp. 938-945 ◽  
Author(s):  
Gerhard Hermann ◽  
Georg Rainer-Harbach ◽  
Siegfried Steeb
Keyword(s):  
Critical Point ◽  
Small Angle ◽  
Lattice Gas ◽  
Critical Concentration ◽  
Mean Field Theory ◽  
Mean Field ◽  
Small Angle Scattering ◽  
Correlation Lengths ◽  
X Ray ◽  
Angle Scattering

Abstract X-ray small-angle scattering experiments were performed on nine melts of the Cd-Ga system at different temperatures up to 440°C. Evaluation of the data follows the Ornstein-Zernike theory of critical scattering, thus yielding correlation lengths ξ of concentration fluctuations and the long-wavelength limit Sec (0) of the Bhatia-Thornton structure factor. Studies of the concentration and temperature dependence of ξ and SCC (0) indicate that the critical point occurs at cc = 50.0 ± 1-0 at % Ga and Tc - 295.2 ± 0-1° C. For a melt with the critical concentration, SCC (0) increases up to 3500 times the ideal S1dCC (0)=CACB-This indicates a strong segregation tendency. In the vicinity of the critical point of the Cd-Ga system, experimental correlation lengths ξ > 100 A were obtained. The critical-point exponents ν and γ were determined. It follows that the behaviour of a critical Cd-Ga melt satisfies the prediction of the classical mean-field theory for higher temperatures, whereas, within experimental accuracy, the lattice-gas predictions are satisfied upon approaching the critical temperature.

A comparison of the correlation structure in GPR images of deltaic and barrier‐spit depositional environments

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1142-1153 ◽  
Author(s):  
Paulette Tercier ◽  
Rosemary Knight ◽  
Harry Jol
Keyword(s):  
Correlation Length ◽  
Ground Penetrating Radar ◽  
Depositional Environments ◽  
Geostatistical Analysis ◽  
Maximum Correlation ◽  
Correlation Lengths ◽  
Correlation Structures ◽  
Geostatistical Models ◽  
Ground Penetrating ◽  
Radar Facies

We have used geostatistical analysis of radar reflections to quantify the correlation structures found in 2-D ground‐penetrating radar (GPR) images. We find that the experimental semivariogram, the product of the geostatistical analysis of the GPR data, is well‐defined and can be modeled using standard geostatistical models to obtain an estimate of the range or correlation length, and the maximum correlation direction, in the 2-D GPR image. When we compare the results from geostatistical analysis of GPR data from selected deltaic and barrier‐spit depositional environments we find different correlation structures in GPR images from different depositional environments. GPR images from braid deltas have near‐horizontal correlation directions and correlation lengths on the order of a few meters. In contrast, the GPR image of a fan‐foreset delta has a very long (>24 m) correlation length and a maximum correlation direction plunging 20°. In the GPR images from barrier spits, we find maximum correlation directions that are horizontal or plunging a few degrees. The correlation lengths range from 7 to 43 m, depending on the orientation of the GPR image relative to spit end growth, and on the specific radar facies that is analyzed.

scholarly journals On the Role of Curved Membrane Nanodomains and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

2021 ◽  
Vol 22 (5) ◽  
pp. 2348
Author(s):  
Luka Mesarec ◽  
Mitja Drab ◽  
Samo Penič ◽  
Veronika Kralj-Iglič ◽  
Aleš Iglič
Keyword(s):  
Actin Cytoskeleton ◽  
Cell Shape ◽  
Critical Concentration ◽  
Equilibrium Shape ◽  
Orientation Angle ◽  
Membrane Skeleton ◽  
Membrane Protrusions ◽  
Membrane Budding ◽  
Curved Membrane

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Spatial correlation length of normalized cone data in sand: case study in the north of Denmark

2014 ◽  
Vol 51 (8) ◽  
pp. 844-857 ◽  
Author(s):  
S. Firouzianbandpey ◽  
D.V. Griffiths ◽  
L.B. Ibsen ◽  
L.V. Andersen
Keyword(s):  
Spatial Correlation ◽  
Correlation Length ◽  
Vertical Direction ◽  
Cone Penetration ◽  
Correlation Lengths ◽  
Cone Penetration Testing ◽  
The North ◽  
Site Investigations ◽  
Depositional Process ◽  
Spatial Correlation Length

The main topic of this study is to assess the anisotropic spatial correlation lengths of a sand layer deposit based on cone penetration testing with pore pressure measurement (CPTu) data. Spatial correlation length can be an important factor in reliability analysis of geotechnical systems, yet it is rarely estimated during routine site investigations. Results from two different sites in the north of Denmark are reported in this paper, indicating quite strong anisotropy due to the depositional process, with significantly shorter spatial correlation lengths in the vertical direction. It is observed that the normalized cone resistance is a better estimator of spatial trends than the normalized friction ratio.

Role of boron on grain sizes and magnetic correlation lengths in recording media as determined by soft x-ray scattering

2002 ◽  
Vol 80 (7) ◽  
pp. 1234-1236 ◽  
Author(s):  
Olav Hellwig ◽  
D. T. Margulies ◽  
B. Lengsfield ◽  
Eric E. Fullerton ◽  
J. B. Kortright
Keyword(s):  
Recording Media ◽  
Correlation Lengths ◽  
X Ray ◽  
Magnetic Correlation ◽  
Grain Sizes ◽  
X Ray Scattering ◽  
Ray Scattering

The gaseous oxidation of aliphatic alcohols. I. Ethyl alcohol: the products formed in the early stages

1956 ◽  
Vol 237 (1211) ◽  
pp. 530-542 ◽  
Keyword(s):  
Hydrogen Peroxide ◽  
Induction Period ◽  
Ethyl Alcohol ◽  
Critical Concentration ◽  
Volume Ratio ◽  
Analytical Investigation ◽  
Moderate Increase ◽  
Early Stages ◽  
Low Pressures

A detailed analytical investigation has been made of the reactions occurring during the early stages of the oxidation of ethyl alcohol (ethanol) in the temperature region 270 to 370° C. During an induction period the alcohol is converted quantitatively into acetaldehyde until a critical concentration of this intermediate has accumulated. The pressure then begins to rise autocatalytically, and methanol, formaldehyde and carbon monoxide become detectable; evidence is presented to show that these compounds arise from the further oxidation of acetaldehyde. The amount of ethanol consumed and of acetaldehyde formed at the end of the induction period are largely independent of the initial reactant pressures, except at low pressures of the alcohol. A study of the effect of added acetaldehyde shows that the minimum quantity required to eliminate the induction period is the same as that normally present at the end of the induction period. Hydrogen peroxide is the only product, other than acetaldehyde, detected during the induction period. Under optimum surface conditions the yields of hydrogen peroxide are equivalent to those of the aldehyde. A moderate increase in surface shortens the induction period, but a further increase retards reaction. In vessels of large surface: volume ratio, the yields of hydrogen peroxide are much reduced, while in a potassium chloride-coated vessel peroxides are invariably absent; in each case, the other products are unchanged. The mechanisms of the chain-initiating and propagating reactions are considered and the role of the surface in initiating and terminating chains is discussed.

LONGITUDINAL CORRELATION LENGTH IN DIRECTED PERCOLATION AND RELATED MODELS: A POSSIBLE NEW SCALING MECHANISM

1991 ◽  
Vol 05 (08) ◽  
pp. 555-559 ◽  
Author(s):  
MALTE HENKEL ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Long Range ◽  
Correlation Length ◽  
Finite Size ◽  
Directed Percolation ◽  
Long Range Order ◽  
Finite Size Scaling ◽  
Asymptotic Behaviors ◽  
Longitudinal Correlation ◽  
Asymptotic Eigenvalue ◽  
Asymptotic Scaling

The finite-size scaling of the correlation length for directed and undirected systems is reviewed with emphasis on the asymptotic eigenvalue degeneracy associated with long-range order or long-range connectivity. The standard scaling mechanism for matching asymptotic behaviors on approach to criticality applies for Ising and other models. However, numerical evidence suggests that for directed percolation in 2D a modified formulation is appropriate, incorporating irrelevant-variable corrections in a new pattern of asymptotic scaling.

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