A percolation system with extremely long range connections and node dilution

We study the very long-range bond-percolation problem on a linear chain with both sites and bonds dilution. Very long range means that the probability $p_{ij}$ for a connection between two occupied sites $i,j$ at a distance $r_{ij}$ decays as a power law, i.e. $p_{ij} = \rho/[r_{ij}^\alpha N^{1-\alpha}]$ when $0 \le \alpha < 1$, and $p_{ij} = \rho/[r_{ij} \ln(N)]$ when $\alpha = 1$. Site dilution means that the occupancy probability of a site is $0 < p_s \le 1$. The behavior of this model results from the competition between long-range connectivity, which enhances the percolation, and site dilution, which weakens percolation. The case $\alpha=0$ with $p_s =1$ is well-known, being the exactly solvable mean-field model. The percolation order parameter $P_\infty$ is investigated numerically for different values of $\alpha$, $p_s$ and $\rho$. We show that in the ranges $0 \le \alpha \le 1$ and $0 < p_s \le 1$ the percolation order parameter $P_\infty$ depends only on the average connectivity $\gamma$ of sites, which can be explicitly computed in terms of the three parameters $\alpha$, $p_s$ and $\rho$

Comments on ππ phase shifts as determined from the peripheral model

The determination of the S-wave ππ phase shifts δ0I at low energy from the analysis of πN→(2π)N is examined critically from the standpoint of the one-pion-exchange model with absorptive corrections. It is found that: (1) The value of δ0I depends strongly on the P-wave phase shifts, which cannot be unambiguously determined, at mππ&lt;600 MeV, by using a Breit-Wigner formula. (2) The ratio of the production density matrix elements ρ (with the ππ elastic scattering amplitudes factored out) depends strongly on mππ for mππ&lt;600 MeV. (3) The (F-B)(F+B) asymmetry shows a sizeable dependence on the momentum transfer t to the nucleon. It is concluded that more accurate data at low mππ are required in order to determine δ0I for mππ&lt;600 MeV. Tables of the ρ(mππ,A t) calculated from the absorption model for an incident-pion laboratory kinetic energy of 4 BeV are included. These could be directly applied to the data to obtain the low-energy ππ phase shifts. © 1968 The American Physical Society

Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function $f(l)$ . Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function $f(l)$. The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function $f(l)$. Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet.Comment: 6 pages, 6 figures, to appear in EPJ

Majority-Vote Model on a Random Lattice

The stationary critical properties of the isotropic majority vote model on random lattices with quenched connectivity disorder are calculated by using Monte Carlo simulations and finite size analysis. The critical exponents $\gamma$ and $\beta$ are found to be different from those of the Ising and majority vote on the square lattice model and the critical noise parameter is found to be $q_{c}=0.117\pm0.005$.Comment: 4 pages, 6 figure

Personal experience with the remote check telehealth in cochlear implant users: from COVID-19 emergency to routine service

Purpose: To critically illustrate the personal experience with using the “Remote Check” application which remotely monitors the hearing rehabilitation level of cochlear implant users at home and further allows clinicians to schedule in-clinic sessions according to the patients’ needs. Methods: 12-month prospective study. Eighty adult cochlear implant users (females n = 37, males n = 43; age range 20–77&nbsp;years) with ≥ 36&nbsp;months of cochlear implant experience and ≥ 12&nbsp;months of stable auditory and speech recognition level volunteered for this 12-month long prospective study. For each patient, at the beginning of the study during the in-clinic session to assess the stable aided hearing thresholds and the cochlear implant integrity and patient’s usage, the “Remote Check” assessment baseline values were obtained. “Remote Check” outcomes were collected at different times in the subsequent at-home sessions, to identify the patients that had to reach the Center. Chi-square test has been used for statistical analysis of the comparison of the “Remote Check” outcomes and in-clinic session results. Results: “Remote Check” application outcomes demonstrated minimal or no differences between all sessions. The at-home Remote Check application reached the same clinical outcomes as the in-clinic sessions in 79 out 80 of participants (99%) with high statistical significance (p &lt; 0.05). Conclusions: “Remote Check” application supported hearing monitoring in cochlear implant users that were not able to attend the in-clinic review during COVID-19 pandemic time. This study demonstrates that the application can be a useful routine tool also for clinical follow-up of cochlear implant users with stable aided hearing

Pair contact process with diffusion of pairs

The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class, despite the fact that the PCP possesses infinitely many absorbing configurations whereas the CP has but one. The critical behavior of the PCP with hopping by particles (PCPD) is as yet unclear. Here we study a version of the PCP in which nearest-neighbor particle {\it pairs} can hop but individual particles cannot. Using quasistationary simulations for three values of the diffusion probability ($D=0.1$, 0.5 and 0.9), we find convincing evidence of DP-like critical behavior.Comment: 9 pages, 3 figure