Equilibrium Properties of A Monomer-Monomer Catalytic Reaction on A One-Dimensional Chain

We study the equilibrium properties of a lattice-gas model of an $A + B \to 0$ catalytic reaction on a one-dimensional chain in contact with a reservoir for the particles. The particles of species $A$ and $B$ are in thermal contact with their vapor phases acting as reservoirs, i.e., they may adsorb onto empty lattice sites and may desorb from the lattice. If adsorbed $A$ and $B$ particles appear at neighboring lattice sites they instantaneously react and both desorb. For this model of a catalytic reaction in the adsorption-controlled limit, we derive analytically the expression of the pressure and present exact results for the mean densities of particles and for the compressibilities of the adsorbate as function of the chemical potentials of the two species.Comment: 19 pages, 5 figures, submitted to Phys. Rev.

A mean-field kinetic lattice gas model of electrochemical cells

We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier work for neutral particles. We include the Poisson equation to account for the influence of the electric field on ion migration, and oxido-reduction processes on the electrode surfaces to allow for growth and dissolution. We confirm the viability of our approach by simulating (i) the electrochemical equilibrium at flat electrodes, which displays the correct charged double-layer, (ii) the growth kinetics of one-dimensional electrochemical cells during growth and dissolution, and (iii) electrochemical dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure

Luminescence spectra and kinetics of disordered solid solutions

We have studied both theoretically and experimentally the luminescence spectra and kinetics of crystalline, disordered solid solutions after pulsed excitation. First, we present the model calculations of the steady-state luminescence band shape caused by recombination of excitons localized in the wells of random potential induced by disorder. Classification of optically active tail states of the main exciton band into two groups is proposed. The majority of the states responsible for the optical absorption corresponds to the group of extended states belonging to the percolation cluster, whereas only a relatively small group of “radiative” states forms the steady-state luminescence band. The continuum percolation theory is applied to distinguish the “radiative” localized states, which are isolated in space and have no ways for nonradiative transitions along the tail states. It is found that the analysis of the exciton-phonon interaction gives the information about the character of the localization of excitons. We have shown that the model used describes quite well the experimental cw spectra of CdS(1−c)Sec and ZnSe(1−c)Tec solid solutions. Further, the experimental results are presented for the temporal evolution of the luminescence band. It is shown that the changes of band shape with time come from the interplay of population dynamics of extended states and spatially isolated “radiative” states. Finally, the measurements of the decay of the spectrally integrated luminescence intensity at long delay times are presented. It is shown that the observed temporal behavior can be described in terms of relaxation of separated pairs followed by subsequent exciton formation and radiative recombination. Electron tunneling processes are supposed to be responsible for the luminescence in the long-time limit at excitation below the exciton mobility edge. At excitation by photons with higher energies the diffusion of electrons can account for the observed behavior of the luminescence

Parameterized scattering matrices for small particles in planetary atmospheres.

Parameterized matrices are discussed that may be used as (single) scattering matrices for interpretations of the brightness and polarization of planetary atmospheres containing randomly oriented small particles. A number of guidelines are developed for the construction of such matrices. These guidelines are based on (i) physical conditions for the elements of a natural scattering matrix, some holding for arbitrary scattering angles and some for the exact forward and backward scattering directions only, as well as (ii) theorems for the asymptotic behavior of coefficients in expansions of the matrix elements in generalized spherical functions of the scattering angle. A set of parameterized matrices is introduced and assessed according to these guidelines. These particular parameterizations are especially useful for scattering by particles that are not large compared to the wavelength, particles in the Rayleigh-Gans domain and for a variety of irregularly shaped particles in the visible part of the spectrum. The use of parameterized matrices as scattering matrices is illustrated by deriving their elements as functions of the scattering angle from simulated measurements of the brightness and polarization of light reflected by plane-parallel atmospheres containing aggregated or spheroidal particles. In both cases, the scattering angle dependences of the original elements are retrieved in fair approximation. © 2001 Elsevier Science Ltd. All rights reserved

Reconstructing the early global dynamics of under-ascertained COVID-19 cases and infections

Background: Asymptomatic or subclinical SARS-CoV-2 infections are often unreported, which means that confirmed case counts may not accurately reflect underlying epidemic dynamics. Understanding the level of ascertainment (the ratio of confirmed symptomatic cases to the true number of symptomatic individuals) and undetected epidemic progression is crucial to informing COVID-19 response planning, including the introduction and relaxation of control measures. Estimating case ascertainment over time allows for accurate estimates of specific outcomes such as seroprevalence, which is essential for planning control measures. Methods: Using reported data on COVID-19 cases and fatalities globally, we estimated the proportion of symptomatic cases (i.e. any person with any of fever ≥ 37.5 °C, cough, shortness of breath, sudden onset of anosmia, ageusia or dysgeusia illness) that were reported in 210 countries and territories, given those countries had experienced more than ten deaths. We used published estimates of the baseline case fatality ratio (CFR), which was adjusted for delays and under-ascertainment, then calculated the ratio of this baseline CFR to an estimated local delay-adjusted CFR to estimate the level of under-ascertainment in a particular location. We then fit a Bayesian Gaussian process model to estimate the temporal pattern of under-ascertainment. Results: Based on reported cases and deaths, we estimated that, during March 2020, the median percentage of symptomatic cases detected across the 84 countries which experienced more than ten deaths ranged from 2.4% (Bangladesh) to 100% (Chile). Across the ten countries with the highest number of total confirmed cases as of 6 July 2020, we estimated that the peak number of symptomatic cases ranged from 1.4 times (Chile) to 18 times (France) larger than reported. Comparing our model with national and regional seroprevalence data where available, we find that our estimates are consistent with observed values. Finally, we estimated seroprevalence for each country. As of 7 June, our seroprevalence estimates range from 0% (many countries) to 13% (95% CrI 5.6–24%) (Belgium). Conclusions: We found substantial under-ascertainment of symptomatic cases, particularly at the peak of the first wave of the SARS-CoV-2 pandemic, in many countries. Reported case counts will therefore likely underestimate the rate of outbreak growth initially and underestimate the decline in the later stages of an epidemic. Although there was considerable under-reporting in many locations, our estimates were consistent with emerging serological data, suggesting that the proportion of each country’s population infected with SARS-CoV-2 worldwide is generally low