Related papers: The atomic ionization, capture, and stopping cross…
The previously applied independent atom model (IAM) for highly charged ion-molecule collisions which implemented the suppression of multiple ionization and capture on the basis of geometric overlaps of cross-sectional areas representing…
Benford's law is widely used for fraud-detection nowadays. The underlying assumption for using the law is that a "regular" dataset follows the significant digit phenomenon. In this paper, we address the scenario where a shrewd fraudster…
Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that…
Infrared spectra of various polymers were treated statistically. It was established that for the absorbance spectra the Benford distribution of leading digits takes place, whereas the distribution of leading digits for transmittance spectra…
Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to…
Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11\% of the time, as one would expect if all digits were equally likely, but rather 30\%. This phenomenon is known…
Questions are raised about certain experimental and theoretical claims that atoms may be stabilized into their bound states, and prevented from achieving full ionization, by the application of adiabatic, ultraintense, high-frequency laser…
The probability that a number in many naturally occurring tables of numerical data has first significant digit $d$ is predicted by Benford's Law ${\rm Prob} (d) = \log_{10} (1 + {\displaystyle{1\over d}}), d = 1, 2 >..., 9$. Illustrations…
We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the…
The original binary-encounter Bethe model of Kim and Eugene Rudd (1994 Phys. Rev. A 50 3954-67) has proven to be an accurate analytical representation of total impact ionisation cross sections of electrons colliding with atoms and…
The energy losses at collisions of heavy multiplycharged ions with light atoms have been considered under circumstances the ion charge Z>>1 and the relative colliding velocity v>>1, so that Z~v=<c, where c - the light velocity (atomic units…
Benford's law predicts the occurrence of the $n^{\mathrm{th}}$ digit of numbers in datasets originating from various sources of the world, ranging from financial data to atomic spectra. It is intriguing that although many features of…
We apply a recently introduced model for an independent-atom-like calculation of ion-impact electron transfer and ionization cross sections to proton collisions from water, neon, and carbon clusters. The model is based on a geometrical…
Benford's law is frequently used to evaluate the likihood that data is misrepresentative. Typically statistical tests measure the likihood. Another method of employing Benford's law is to compare the frequency of leading digits to the…
We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the…
Benford's Law predicts that the first significant digit on the leftmost side of numbers in real-life data is proportioned between all possible 1 to 9 digits approximately as in LOG(1 + 1/digit), so that low digits occur much more frequently…
Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability.…
A century ago, it was predicted that the first significant digit appearing in a data would be nonuniformly distributed, with the number one appearing with the highest frequency. This law goes by the name of Benford's law. It holds for data…
Nature and our world have a bias! Roughly $30\%$ of the time the number $1$ occurs as the leading digit in many datasets base $10$. This phenomenon is known as Benford's law and it arrises in diverse fields such as the stock market,…
At high energies, in particle-capture processes between ions and atoms, classical kinematic requirements show that generally double collision Thomas processes dominate. However, for certain mass-ratios these processes are kinematically…