Search results for "fractal dimension."
showing 10 items of 75 documents
Dimensionality Dependence of the Metal-Insulator Transition in the Anderson Model of Localization
1996
The metal-insulator transition is investigated by means of the transfer-matrix method to describe the critical behavior close to the lower critical dimension 2. We study several bifractal systems with fractal dimensions between 2 and 3. Together with 3D and 4D results, these data give a coherent description of the dimensionality dependence of the critical disorder and the critical exponent in terms of the spectral dimension of the samples. We also show that the upper critical dimension is probably infinite, certainly larger than 4.
Surface tension and interfacial fluctuations in d-dimensional Ising model
2005
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)…
Non-equilibrium temperature of well-developed quantum turbulence
2009
Abstract A non-equilibrium effective temperature of quantum vortex tangles is defined as the average energy of closed vortex loops. The resulting thermodynamic expressions for the entropy and the energy in terms of the temperature of the tangle are confirmed by a microscopic analysis based on a potential distribution function for the length of vortex loops. Furthermore, these expressions for the entropy and energy in terms of temperature are analogous to those of black holes: this may be of interest for establishing further connections between topological defects in superfluids and cosmology.
Fractal dimension of superfluid turbulence : A random-walk toy model
2021
This paper deals with the fractal dimension of a superfluid vortex tangle. It extends a previous model [J. Phys. A: Math. Theor. {\bf 43}, 205501 (2010)] (which was proposed for very low temperature), and it proposes an alternative random walk toy model, which is valid also for finite temperature. This random walk model combines a recent Nemirovskii's proposal, and a simple modelization of a self-similar structure of vortex loops (mimicking the geometry of the loops of several sizes which compose the tangle). The fractal dimension of the vortex tangle is then related to the exponents describing how the vortex energy per unit length changes with the length scales, for which we take recent pr…
Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
1992
In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.
Valence Topological Charge-Transfer Indices for Dipole Moments
2003
Valence topological charge-transfer (CT) indices are applied to the calculation of dipole moments. The dipole moments calculated by algebraic and vector semisums of the CT indices are defined. The combination of the CT indices allows the estimation of the dipole moments. The model is generalized for molecules with heteroatoms. The ability of the indices for the description of the molecular charge distribution is established by comparing them with the dipole moment of the valence-isoelectronic series of benzene and styrene. Two CT indices, μ v e c (vector semisum of vertex-pair dipole moments) and μ V v e c (valence μ v e c ) are proposed. μ v e c and μ V v e c are important for the predicti…
QSPR prediction of chromatographic retention times of pesticides: Partition and fractal indices
2014
The high-performance liquid-chromatographic retentions of red-wine pesticide residues are modeled by structure-property relationships. The effect of different types of features is analyzed: geometric, lipophilic, etc. The properties are fractal dimensions, partition coefficient, etc., in linear and nonlinear correlation models. Biological plastic evolution is an evolutionary perspective conjugating the effect of acquired characters and relations that emerge among the principles of evolutionary indeterminacy, morphological determination and natural selection. It is applied to design the co-ordination index that is used to characterize pesticide retentions. The parameters used to calculate th…
SELF SIMILARITY IN SWELLING SYSTEMS: FRACTAL PROPERTIES OF PEAT
1994
Sphagnum peat gives an example of a swelling system with a self-similar structure in sufficiently wide range of scales. The surface fractal dimension, dfs, has been calculated by means of thermodynamic method on the basis of water adsorption and capillary equilibrium measurements. This method makes possible the exploration of the self-similarity in the scale range over at least 4 decimal orders of magnitude from 1 nm to 10 μm. In a sample explored, two ranges of fractality have been observed: dfs ≈ 2.55 in the range 1.5–80 nm and dfs ≈ 2.42 in the range 0.25–9 µm.
Reproducibility and accuracy in the morphometric and mechanical quantification of trabecular bone from 3Tesla magnetic resonance images
2014
Abstract Objective We used an animal model to analyze the reproducibility and accuracy of certain biomarkers of bone image quality in comparison to a gold standard of computed microtomography (μCT). Materials and methods We used magnetic resonance (MR) imaging and μCT to study the metaphyses of 5 sheep tibiae. The MR images (3 T) were acquired with a T1-weighted gradient echo sequence and an isotropic spatial resolution of 180 μm. The μCT images were acquired using a scanner with a spatial resolution of 7.5 μm isotropic voxels. In the preparation of the images, we applied equalization, interpolation, and thresholding algorithms. In the quantitative analysis, we calculated the percentage of …
Characterizing cavity-like spaces in active-site models of zeolites
2003
A method for the calculation of fractal surfaces of crystals is presented. The fractal dimension of fragments of zeolites is computed. Results compare well with reference calculations performed with program GEPOL. The active site of Bronsted acid zeolites is modelled by sets of Al–OH–Si units. These units form 2–12-membered rings. Topological indices for the different active-site models are computed. The comparison of calculations performed with programs GEPOL and SURMO2 allows computing the model indices. The cavity-like globularity and rugosity show sharp discontinuities for the ring with 6 units. Most cavity-like spaces show no fractal character. However, the 6–8-ring cavity-like spaces …