We prove a distributional limit theorem conjectured in Clark (J Stat Phys 174(6):1372–1403, 2019) for partition functions defining models of directed polymers on diamond hierarchical graphs with disorder variables placed at the graphical edges. The limiting regime involves joint scaling which number layers, \(n\in {\mathbb {N}}\), grows as inverse temperature, \(\beta \equiv \beta (n)\), vanish...

BACKGROUND The purpose of this study was to quantify the heterogeneous distribution of echodensities in the pericardial fluid of patients with tuberculous pericarditis using echocardiography and fractal analysis, and to determine whether there were differences in the fractal dimensions of effusive-constrictive and effusive non-constrictive disease. METHODS We used fractal geometry to quantify...

Isothermal kinetics of the exchange absorbed water in a silica hydrogel (SH) with ethanol was examined. The isothermal kinetic curves were measured at temperatures: T = 297, 306 and 316 K. rate analysed as function time. possibility mathematical description by Brouers Sotolongo-Costa?s (BS) fractal?s model Parameter values (n, ?, ?) their changes temperature calculated. By applying method Ozao,...

Planners and designers are interested in replicating biospheric landscape patterns to reclaim surface mines to match existing natural landscape patterns. One approach that shows promise is the use of fractal geometry to generate biospheric landscape patterns. While the measurement of the actual fractal dimension of a landscape can be difficult, a box-counting method was developed at AgroCampus ...

Our goal is to store S (a set of keys) in such a way that we can quickly (i.e. with few memory accesses) answer queries of the form “Is i ∈ S?”. So we want to encode S in a table via some encoding scheme S → E(S). An algorithm for the membership problem takes a query “Is i ∈ S” and makes a few ‘probes’ into the table E(S), where a probe is just an index (cell) in the table. Based on the values ...

With aging and disease, there is a breakdown of the natural fractal-like organization of heart rate (HR). Fractal-like correlation properties of HR can be assessed with detrended fluctuation analysis (DFA). A short-time scaling exponent (alpha(s)) value of 1 is associated with healthy HR dynamics, whereas values that deviate away from 1, in either direction, indicate fractal collapse. The purpo...

In this paper, an interaction of metal nanoparticles that appears in the extinction spectra was investigated. The mutual coupling between the nanoparticles, the effect of size difference, and the interparticle separation in silver nanoparticle dimers are studied by computer discrete dipole approximation methods. The obtained results show that nanoparticle interaction results in the distinct col...

The capillary pressure model proposed empirically by Brooks and Corey has been used widely for several decades. However it is not clear why the Brooks-Corey capillary pressure model works so well. In this study, it has been found that the empirical Brooks-Corey capillary pressure model can be derived theoretically from fractal modeling of porous media. Also found was the correlation between the...