Hurst's empirical law in the probability of atomic distribution in liquids

Hurst's Exponent Determination for Radial Distribution Functions of In, Sn and In-40 wt%Sn Melt

“…Thus, a number of atoms within the short range scope, not the full extent, follow fractional Brownian motion with strong persistency, which is different from Ref. [11]. The reason is that within the short range, the liquid structure is directly related to an interaction potential with an attractive part, atoms arrange in a orderly manner.…”

“…Thus, compared to Ref. [11], the interpretation that the 𝐻 value was treated as an indicator of temperature-induced liquidliquid structure transition is controversial. For the same metal melt at different temperatures, 𝐻 exhibits tiny changes, which may be generated by the noise or some error in the data treatment.…”

“…The strength of the persistence increases as 𝐻 approaches 1, with the correlation measure presenting high positive values, these series are considered to follow a biased random walk or fractional Brownian motion. [11] 150 In other words, if the RDF curve exhibits self-similar scaling behavior, log(𝑅/𝑆) as a function of log𝜏 will result in a straight line, with 𝐻 as the slope. The 120505-2 horizontal coordinate 𝜏 of the dashed line is 0.24 nm for In melt, 0.23 nm for Sn and In-40 wt%Sn melts.…”

“…According to Refs. [11,16], the 𝑉 -statistics 𝑉 𝜏 is used to describe the stability of 𝑅/𝑆 analysis on RDF serials and measure the length of the nonperiodic long-term correlation. 𝑉 𝜏 is expressed as…”

“…In the 𝑉 𝜏 -log 𝜏 graph, the distance from the initial to the turning point is a non-periodic cycle, 𝜏 at the turning point is the average cycle length. [11,17] The average cycle lengths (𝑇 cycle ) of RDF serials within short range 120505-3 scope for In, Sn and In-40 wt%Sn melts are shown in Fig. 3.…”