Diffusion as a First Model of Spread of Viral Infection

The appearance of the coronavirus (COVID-19) in late 2019 has dominated the news in the last few months as it developed into a pandemic. In many mathematics and physics classrooms, instructors are using the time series of the number of cases to show exponential growth of the infection. In this manuscript we propose a simple diffusion process as the mode of spreading infections. This model is less sophisticated than other models in the literature, but it can capture the exponential growth and it can explain it in terms of mobility (diffusion constant), population density, and probability of transmission. Students can change the parameters and determine the growth rate and predict the total number of cases as a function of time. Students are also given the opportunity to add other factors that are not considered in the simple diffusion model

Effects of randomization of characteristic times on spiral wave generation in a simple cellular automaton model of excitable media

Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions such as epilepsy and atrial fibrillation. We used a simple cellular automaton model to study propagation in excitable media, with a particular focus in understanding spiral wave behavior. The main ingredients of this cellular automaton model are an excitation condition and characteristic excitation and refractory periods. The literature shows that fixed excitation and refractory periods together with specific initial conditions generate stationary and stable spiral waves. In the present work we allowed the activation and refractory periods to fluctuate uniformly over a range of values. Under these conditions formed spiral waves might drift, the wave front might break, and in some extreme cases it might lead to a complete breakdown of the spiral pattern.Comment: 15 pages, 14 Figures, 18 reference

Predicting the Photoelectron Spectra of Quasi Octahedral Al6Mo\u3csup\u3e-\u3c/sup\u3e Cluster

We have recently developed a computational methodology to separate the effects of size, composition, symmetry and fluxionality in explaining the experimental photoelectron spectra of mixed-metal clusters. This methodology was successfully applied first in explaining the observed differences between the spectra of Al13- and Al12Ni- and more recently to explain the measured spectra of AlnMo-, n=3–5,7 clusters. The combination of our approach and new synthesis techniques can be used to prepare cluster-based materials with tunable properties. In this work we use the methodology to predict the spectrum of Al6Mo-. This system was chosen because its neutral counterpart is a perfect octahedron and it is distorted to a D3d symmetry and was not observed in the recent experiments. This high symmetry cluster bridges the less symmetric Al5Mo- and Al7Mo-structures.The measured spectra of Al5Mo- has well defined peaks, while that of Al7Mo-does not. This can be explained by the fluxionality of Al7Mo-, as at least 6 different structures lie within the range that can be reached by thermal effects. We predict that Al6Mo- has well defined peaks, but some broadening is expected as there are two low-lying isomers, one of D3d and the second of D3h symmetry that are only 0.052 eV apart

Diffusion as a first model of spread of viral infection

The appearance of the coronavirus (COVID-19) in late 2019 has dominated the news in the last few months as it developed into a pandemic. In many mathematics and physics classrooms, instructors are using the time series of the number of cases to show exponential growth of the infection. In this manuscript, we propose a simple diffusion process as the mode of spreading infections. This model is less sophisticated than other models in the literature, but it can capture the exponential growth and it can explain it in terms of mobility (diffusion constant), population density, and probability of transmission. Students can change the parameters and determine the growth rate and predict the total number of cases as a function of time. Students are also given the opportunity to add other factors that are not considered in the simple diffusion model

Predicting the Photoelectron Spectra of Quasi Octahedral Al6Mo\u3csup\u3e-\u3c/sup\u3e Cluster

We have recently developed a computational methodology to separate the effects of size, composition, symmetry and fluxionality in explaining the experimental photoelectron spectra of mixed-metal clusters. This methodology was successfully applied first in explaining the observed differences between the spectra of Al13- and Al12Ni- and more recently to explain the measured spectra of AlnMo-, n=3–5,7 clusters. The combination of our approach and new synthesis techniques can be used to prepare cluster-based materials with tunable properties. In this work we use the methodology to predict the spectrum of Al6Mo-. This system was chosen because its neutral counterpart is a perfect octahedron and it is distorted to a D3d symmetry and was not observed in the recent experiments. This high symmetry cluster bridges the less symmetric Al5Mo- and Al7Mo-structures.The measured spectra of Al5Mo- has well defined peaks, while that of Al7Mo-does not. This can be explained by the fluxionality of Al7Mo-, as at least 6 different structures lie within the range that can be reached by thermal effects. We predict that Al6Mo- has well defined peaks, but some broadening is expected as there are two low-lying isomers, one of D3d and the second of D3h symmetry that are only 0.052 eV apart

Diffusion as a first model of spread of viral infection

The appearance of the coronavirus (COVID-19) in late 2019 has dominated the news in the last few months as it developed into a pandemic. In many mathematics and physics classrooms, instructors are using the time series of the number of cases to show exponential growth of the infection. In this manuscript, we propose a simple diffusion process as the mode of spreading infections. This model is less sophisticated than other models in the literature, but it can capture the exponential growth and it can explain it in terms of mobility (diffusion constant), population density, and probability of transmission. Students can change the parameters and determine the growth rate and predict the total number of cases as a function of time. Students are also given the opportunity to add other factors that are not considered in the simple diffusion model

A computational study of Al

Results of density functional theory calculations on Aln− and Aln−1Pt−, n = 2–8, clusters are presented and analyzed. The analysis includes different structural forms of the clusters characterized in terms of binding energy, spin and symmetry, and a comparative evaluation of various properties of the two systems viewed as connected through a single-Pt substitutional doping and examined in terms of their respective most stable structures. The Aln−1Pt− clusters are then used as a paradigmatic (model) case of single-atom nanocatalysts, with Pt as the catalytic center and Aln−1 as its support, to implement a uniform descriptor for gauging the tuning effects of all the parameters (“knobs”) of a nanocatalyst that include the identity of the active center and the material and size of its support

Silver- and Gold-Mediated Nucleobase Bonding

We report the results of a density functional theory investigation of the bonding of nucleobases mediated by silver and gold atoms in the gas phase. Our calculations use the Becke exchange and Perdew–Wang correlation functional (BPW91) combined with the Stuttgart effective core potentials to represent the valence electrons of gold, silver, and platinum, and the all-electron DGTZVP basis set for C, H, N, and O. This combination was chosen based on tests on the metal atoms and tautomers of adenine, cytosine, and guanine. To establish a benchmark to understand the metal-mediated bonding, we calculated the binding energy of each of the base pairs in their canonical forms. Our calculations show rather strong bonds between the Watson–Crick base pairs when compared with typical values for N–H–N and N–H–O hydrogen bonds. The neutral metal atoms tend to bond near the nitrogen atoms. The effect of the metal atoms on the bonding of nucleobases differs depending on whether or not the metal atoms bond to one of the hydrogen-bonding sites. When the silver or gold atoms bond to a non-hydrogen-bonding site, the effect is a slight enhancement of the cytosine–guanine bonding, but there is almost no effect on the adenine–thymine pairing. The metal atoms can block one of the hydrogen-bonding sites, thus preventing the normal cytosine–guanine and adenine–thymine pairings. We also find that both silver and gold can bond to consecutive guanines in a similar fashion to platinum, albeit with a significantly lower binding energy