Criticality and Continuity of Explosive Site Percolation in Random Networks

This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i). For any specific $m$, the critical percolation point scales with the average degree of the network while its exponent associated with $m$ is bounded by -1 and $\sim-0.5$. ii). Discontinuous percolation could occur on sparse networks if and only if $m$ approaches infinite. These results not only generalize some conclusions of ordinary percolation but also provide new insights to the network robustness.Comment: 5 pages, 5 figure

Experimental and Numerical Investigation on Progressive Collapse Resistance of Post-tensioned Precast Concrete Beam-Column Sub-assemblages

In this paper, four 1/2 scaled precast concrete (PC) beam-column sub-assemblages with high performance connection were tested under push-down loading procedure to study the load resisting mechanism of PC frames subjected to different column removal scenarios. The parameters investigated include the location of column removal and effective prestress in tendons. The test results indicated that the failure modes of unbonded post-tensioned precast concrete (PTPC) frames were different from that of reinforced concrete (RC) frames: no cracks formed in the beams and wide opening formed near the beam to column interfaces. For specimens without overhanging beams, the failure of side column was eccentric compression failure. Moreover, the load resisting mechanisms in PC frames were significantly different from that of RC frames: the compressive arch action (CAA) developed in concrete during column removal was mainly due to actively applied pre-compressive stress in the concrete; CAA will not vanish when severe crush in concrete occurred. Thus, it may provide negative contribution for load resistance when the displacement exceeds one-beam depth; the tensile force developed in the tendons could provide catenary action from the beginning of the test. Moreover, to deeper understand the behavior of tested specimens, numerical analyses were carried out. The effects of concrete strength, axial compression ratio at side columns, and loading approaches on the behavior of the sub-assemblages were also investigated based on validated numerical analysis

Prompt Iron Enrichment, Two r-Process Components, and Abundances in Very Metal-Poor Stars

We present a model to explain the wide range of abundances for heavy r-process elements (mass number A > 130) at low [Fe/H]. This model requires rapid star formation and/or an initial population of supermassive stars in the earliest condensed clots of matter to provide a prompt or initial Fe inventory. Subsequent Fe and r-process enrichment was provided by two types of supernovae: one producing heavy r-elements with no Fe on a rather short timescale and the other producing light r-elements (A < or = 130) with Fe on a much longer timescale.Comment: 5 pages, 2 postscript figures, to appear in ApJ

Human African trypanosomiasis : the current situation in endemic regions and the risks for non-endemic regions from imported cases

Human African trypanosomiasis (HAT) is caused by Trypanosoma brucei gambiense and T. b. rhodesiense and caused devastating epidemics during the 20th century. Due to effective control programs implemented in the last two decades, the number of reported cases has fallen to a historically low level. Although fewer than 977 cases were reported in 2018 in endemic countries, HAT is still a public health problem in endemic regions until it is completely eliminated. In addition, almost 150 confirmed HAT cases were reported in non-endemic countries in the last three decades. The majority of non-endemic HAT cases were reported in Europe, United States and South Africa, due to historical alliances, economic links or geographic proximity to disease endemic countries. Furthermore, with the implementation of the “Belt and Road” project, sporadic imported HAT cases have been reported in China as a warning sign of tropical diseases prevention. In this paper, we explore and interpret the data on HAT incidence and find no positive correlation between the number of HAT cases from endemic and non-endemic countries.This data will provide useful information for better understanding the imported cases of HAT globally in the post-elimination phase

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

Time dependent diffusion in a disordered medium with partially absorbing walls: A perturbative approach

We present an analytical study of the time dependent diffusion coefficient in a dilute suspension of spheres with partially absorbing boundary condition. Following Kirkpatrick (J. Chem. Phys. 76, 4255) we obtain a perturbative expansion for the time dependent particle density using volume fraction $f$ of spheres as an expansion parameter. The exact single particle $t$-operator for partially absorbing boundary condition is used to obtain a closed form time-dependent diffusion coefficient $D(t)$ accurate to first order in the volume fraction $f$. Short and long time limits of $D(t)$ are checked against the known short-time results for partially or fully absorbing boundary conditions and long-time results for reflecting boundary conditions. For fully absorbing boundary condition the long time diffusion coefficient is found to be $D(t)=5 a^2/(12 f D_{0} t) +O((D_0t/a^2)^{-2})$, to the first order of perturbation theory. Here $f$ is small but non-zero, $D_0$ the diffusion coefficient in the absence of spheres, and $a$ the radius of the spheres. The validity of this perturbative result is discussed

Electron Depletion Due to Bias of a T-Shaped Field-Effect Transistor

A T-shaped field-effect transistor, made out of a pair of two-dimensional electron gases, is modeled and studied. A simple numerical model is developed to study the electron distribution vs. applied gate voltage for different gate lengths. The model is then improved to account for depletion and the width of the two-dimensional electron gases. The results are then compared to the experimental ones and to some approximate analytical calculations and are found to be in good agreement with them.Comment: 16 pages, LaTex (RevTex), 8 fig

Galilean invariance of lattice Boltzmann models

It is well-known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity dependent viscosity. This unphysical dependency violates the Galilean invariance and limits the validation domain of the LB method to near incompressible flows. As previously shown, recovery of correct transport phenomena in kinetic equations depends on the higher hydrodynamic moments. In this Letter, we give specific criteria for recovery of various transport coefficients. The Galilean invariance of a general class of LB models is demonstrated via numerical experiments