Event structure investigation of AuAu interactions from HIJING model using fractal dimensions

This work presents an implementation of fractal geometry methods in the study of event structure for AuAu interactions at collision energies √s _NN = 9.2, 62 and 200 GeV for different interaction dynamics. The events are generated by using the HIJING model. It is shown, that the fractal dimension of events in phase space projections rapidity-transverse momentum (y - p_t) and azimuthal angle-transverse momentum (φ - p_t) are sensitive to the interaction dynamics.     

Radiation friction in fractal clusters

The classical problem of radiation damping is formulated for fractal clusters in terms of interference of radiation friction forces within a small number of aggregated particles, with their interactions being described in the dipole-dipole approximation. The general theory is developed for spherical particles with arbitrary sizes. For particular configurations, the interference nature of the radiation widths of the normal dipole oscillations of aggregates is demonstrated.     

On the theory of optical properties of fractal clusters

A theory of optical properties of clusters of spherical metal nanoparticles characterized by an arbitrary size distribution is developed in a quasi-static dipole approximation. The equations for coupled dipoles and general relations are formulated in terms of reduced dipole moments. It is shown that the dipole resonant frequencies and amplitudes, the absorbed power, and the acting-field magnitudes strongly depend on the ratios of particle radii in a cluster. Properties of linear, planar, and three-dimensional systems are examined.     

Grayscale projection of finite size fractal clusters

The European Physical Journal E - Microscopy techniques are suitable to obtain structural information of colloidal clusters with high resolution, but yield only a two dimensional projection of the...     

Grayscale projection of finite size fractal clusters

Microscopy techniques are suitable to obtain structural information of colloidal clusters with high resolution, but yield only a two dimensional projection of the objects. When imaging finite size objects with fractal properties, such as clusters of colloidal particles, this projection process has to be taken into account for the calculation of the fractal dimension. In this paper we present a technique to calculate the fractal dimension of finite size clusters with fractal properties using grayscale projections such as images obtained by X-ray microscopy. The grayscales are interpreted as different occupation counts within a projection. It is shown, that the radial distribution of these occupation counts varies with the fractal dimension d of the cluster. Using the radius of maximum occupation probability the fractal dimension up to 2.2 of finite size clusters can be calculated. The theoretical predictions are verified by test calculations employing numerically generated clusters.     

Some fractal properties of the percolating backbone in two dimensions

A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that the fractal dimensionality of the backbone isd _f ^BB =1.61±0.01, the chemical dimensionality isd _t=1.40±0.01, and the fractal dimension of the minimum pathd _min=1.15 ± 0.02 for the two-dimensional triangular lattice.     

Output functions and fractal dimensions in dynamical systems

We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the output function evaluation (OFE) method. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with D<0.5, where D is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.     

Analysis of fractal dimensions in the express diagnostics of bacterial colonies

The features of the formation of speckle structures under irradiation of a model fractal (Sierpinski carpet) have been investigated. The relationship between the fractal properties of the diffraction pattern and the scattering structure parameters (model fractal geometrical sizes, fractal depth) has been analyzed for the irradiation by a focused light beam, whose size is comparable with that of the irradiated object. The results of the computer simulation of the Gaussian beam scattering in bacterial colonies are compared with the experimental data.     

Entanglement entropy of highly degenerate States and fractal dimensions

We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a natural geometrical structure. For instance, the spins of a spin-1/2 representation, pointing in various directions, form a sphere. We show that for subsystems with a large number m of local degrees of freedom, the entanglement entropy diverges as d/2 logm, where d is the fractal dimension of the subset of basis elements with nonzero coefficients. We interpret this result by seeing d as the (not necessarily integer) number of zero-energy Goldstone bosons describing the ground state. We suggest that this result holds quite generally for largely degenerate ground states, with potential applications to spin glasses and quenched disorder.