Monitoring and Forecasting COVID-19: Heuristic Regression, Susceptible-Infected-Removed Model and, Spatial Stochastic.

The COVID-19 pandemic has had worldwide devastating effects on human lives, highlighting the need for tools to predict its development. The dynamics of such public-health threats can often be efficiently analyzed through simple models that help to make quantitative timely policy decisions. We benchmark a minimal version of a Susceptible-Infected-Removed model for infectious diseases (SIR) coupled with a simple least-squares Statistical Heuristic Regression (SHR) based on a lognormal distribution. We derive the three free parameters for both models in several cases and test them against the amount of data needed to bring accuracy in predictions. The SHR model is ≈ ±2% accurate about 20 days past the second inflexion point in the daily curve of cases, while the SIR model reaches a similar accuracy a fortnight before. All the analyzed cases assert the utility of SHR and SIR approximants as a valuable tool to forecast the disease's evolution. Finally, we have studied simulated stochastic individual-based SIR dynamics, which yields a detailed spatial and temporal view of the disease that cannot be given by SIR or SHR methods.

Chemical equilibrium in AGB atmospheres: Successes, failures, and prospects for small molecules, clusters, and condensates.

Chemical equilibrium has proven extremely useful for predicting the chemical composition of AGB atmospheres. Here we use a recently developed code and an updated thermochemical database that includes gaseous and condensed species involving 34 elements to compute the chemical equilibrium composition of AGB atmospheres of M-, S-, and C-type stars. We include for the first time Ti x C y clusters, with x = 1-4 and y = 1-4, and selected larger clusters ranging up to Ti13C22, for which thermochemical data are obtained from quantum-chemical calculations. Our main aims are to systematically survey the main reservoirs of each element in AGB atmospheres, review the successes and failures of chemical equilibrium by comparing it with the latest observational data, identify potentially detectable molecules that have not yet been observed, and diagnose the most likely gas-phase precursors of dust and determine which clusters might act as building blocks of dust grains. We find that in general, chemical equilibrium reproduces the observed abundances of parent molecules in circumstellar envelopes of AGB stars well. There are, however, severe discrepancies of several orders of magnitude for some parent molecules that are observed to be anomalously overabundant with respect to the predictions of chemical equilibrium. These are HCN, CS, NH3, and SO2 in M-type stars, H2O and NH3 in S-type stars, and the hydrides H2O, NH3, SiH4, and PH3 in C-type stars. Several molecules have not yet been observed in AGB atmospheres but are predicted with non-negligible abundances and are good candidates for detection with observatories such as ALMA. The most interesting ones are SiC5, SiNH, SiCl, PS, HBO, and the metal-containing molecules MgS, CaS, CaOH, CaCl, CaF, ScO, ZrO, VO, FeS, CoH, and NiS. In agreement with previous studies, the first condensates predicted to appear in C-rich atmospheres are found to be carbon, TiC, and SiC, while Al2O3 is the first major condensate expected in O-rich outflows. According to our chemical equilibrium calculations, the gas-phase precursors of carbon dust are probably acetylene, atomic carbon, and/or C3, while for silicon carbide dust, the most likely precursors are the molecules SiC2 and Si2C. In the case of titanium carbide dust, atomic Ti is the major reservoir of this element in the inner regions of AGB atmospheres, and therefore it is probably the main supplier of titanium during the formation of TiC dust. However, chemical equilibrium predicts that large titanium-carbon clusters such as Ti8C12 and Ti13C22 become the major reservoirs of titanium at the expense of atomic Ti in the region where condensation of TiC is expected to occur. This suggests that the assembly of large Ti x C y clusters might be related to the formation of the first condensation nuclei of TiC. In the case of Al2O3 dust, chemical equilibrium indicates that atomic Al and the carriers of Al-O bonds AlOH, AlO, and Al2O are the most likely gas-phase precursors.

Electron transport in ultra-thin films and ballistic electron emission microscopy.

We have developed a calculation scheme for the elastic electron current in ultra-thin epitaxial heterostructures. Our model uses a Keldysh's non-equilibrium Green's function formalism and a layer-by-layer construction of the epitaxial film. Such an approach is appropriate to describe the current in a ballistic electron emission microscope (BEEM) where the metal base layer is ultra-thin and generalizes a previous one based on a decimation technique appropriated for thick slabs. This formalism allows a full quantum mechanical description of the transmission across the epitaxial heterostructure interface, including multiple scattering via the Dyson equation, which is deemed a crucial ingredient to describe interfaces of ultra-thin layers properly in the future. We introduce a theoretical formulation needed for ultra-thin layers and we compare with results obtained for thick Au(1 1 1) metal layers. An interesting effect takes place for a width of about ten layers: a BEEM current can propagate via the center of the reciprocal space ([Formula: see text]) along the Au(1 1 1) direction. We associate this current to a coherent interference finite-width effect that cannot be found using a decimation technique. Finally, we have tested the validity of the handy semiclassical formalism to describe the BEEM current.

Ortho and para hydrogen dimers on G/SiC(0001): combined STM and DFT study.

The hydrogen (H) dimer structures formed upon room-temperature H adsorption on single layer graphene (SLG) grown on SiC(0001) are addressed using a combined theoretical-experimental approach. Our study includes density functional theory (DFT) calculations for the full (6√3 × 6√3)R30° unit cell of the SLG/SiC(0001) substrate and atomically resolved scanning tunneling microscopy images determining simultaneously the graphene lattice and the internal structure of the H adsorbates. We show that H atoms normally group in chemisorbed coupled structures of different sizes and orientations. We make an atomic scale determination of the most stable experimental geometries, the small dimers and ellipsoid-shaped features, and we assign them to hydrogen adsorbed in para dimers and ortho dimers configuration, respectively, through comparison with the theory.

Diffusion of hydrogen in Pd assisted by inelastic ballistic hot electrons.

Sykes et al. [Proc. Natl. Acad. Sci. U.S.A. 102, 17907 (2005)] have reported how electrons injected from a scanning tunneling microscope modify the diffusion rates of H buried beneath Pd(111). A key point in that experiment is the symmetry between positive and negative voltages for H extraction, which is difficult to explain in view of the large asymmetry in Pd between the electron and hole densities of states. Combining concepts from the theory of ballistic electron microscopy and electron-phonon scattering we show that H diffusion is driven by the s-band electrons only, which explains the observed symmetry.

Understanding atomic-resolved STM images on TiO2(110)-(1 x 1) surface by DFT calculations.

We present a combination of experimental STM images and DFT calculations to understand the atomic scale contrast of features found in high-resolution STM images. Simulating different plausible structural models for the tip, we have been able to reproduce various characteristics previously reported in experimental images on TiO(2)(110)-(1 x 1) under controlled UHV conditions. Our results allow us to determine the influence of different chemical and morphological tip terminations on the atomic-resolution STM images of the TiO(2)(110)-(1 x 1) surface. The commonest images have been properly explained using standard models for a W tip, either clean or with a single O atom located at the apex. Furthermore, a double transfer of oxygen atoms can account for different types of bizarre atomic-resolution features occasionally seen, and not conclusively interpreted before. Importantly, we discuss how typical point-defects are imaged on this surface by different tips, namely bridging O vacancies and adsorbed OH groups.

Interplay between fast diffusion and molecular interaction in the formation of self-assembled nanostructures of S-cysteine on Au(111).

We have studied the first stages leading to the formation of self-assembled monolayers of S-cysteine molecules adsorbed on a Au(111) surface. Density functional theory (DFT) calculations for the adsorption of individual cysteine molecules on Au(111) at room temperature show low-energy barriers all over the 2D Au(111) unit cell. As a consequence, cysteine molecules diffuse freely on the Au(111) surface and they can be regarded as a 2D molecular gas. The balance between molecule-molecule and molecule-substrate interactions induces molecular condensation and evaporation from the morphological surface structures (steps, reconstruction edges, etc.) as revealed by scanning tunnelling microscopy (STM) images. These processes lead progressively to the formation of a number of stable arrangements, not previously reported, such as single-molecular rows, trimers, and 2D islands. The condensation of these structures is driven by the aggregation of new molecules, stabilized by the formation of electrostatic interactions between adjacent NH(3)(+) and COO(-) groups, together with adsorption at a slightly more favorable quasi-top site of the herringbone Au reconstruction.

Ordered vacancy network induced by the growth of epitaxial graphene on Pt(111).

We have studied large areas of (√3×√3)R30° graphene commensurate with a Pt(111) substrate. A combination of experimental techniques with ab initio density functional theory indicates that this structure is related to a reconstruction at the Pt surface, consisting of an ordered vacancy network formed in the outermost Pt layer and a graphene layer covalently bound to the Pt substrate. The formation of this reconstruction is enhanced if low temperatures and polycyclic aromatic hydrocarbons are used as molecular precursors for epitaxial growth of the graphene layers.

Structure of rutile TiO2 (110)-(1 x 2): formation of Ti2O3 quasi-1D metallic chains.

Combining STM, LEED, and density functional theory, we determine the atomic surface structure of rutile TiO2 (110)-(1 x 2): nonstoichiometric Ti2O3 stripes along the [001] direction. LEED patterns are sharp and free of streaks, while STM images show monatomic steps, wide terraces, and no cross-links. At room temperature, atoms in the Ti2O3 group have large amplitudes of vibration. The long quasi-1D chains display metallic character, show no interaction between them, and cannot couple to bulk or surface states in the gap region, forming good atomic wires.

Water dimer diffusion on Pd[111] assisted by an H-bond donor-acceptor tunneling exchange.

Based on the results of density functional theory calculations, a novel mechanism for the diffusion of water dimers on metal surfaces is proposed, which relies on the ability of H bonds to rearrange through quantum tunneling. The mechanism involves quasifree rotation of the dimer and exchange of H-bond donor and acceptor molecules. At appropriate temperatures, water dimers diffuse more rapidly than water monomers, thus providing a physical explanation for the experimentally measured high diffusivity of water dimers on Pd[111] [Science 297, 1850 (2002)]].

General model for water monomer adsorption on close-packed transition and noble metal surfaces.

Ab initio density functional theory has been used to investigate the adsorption of H2O on several close-packed transition and noble metal surfaces. A remarkably common binding mechanism has been identified. On every surface H2O binds preferentially at an atop adsorption site with the molecular dipole plane nearly parallel to the surface. This binding mode favors interaction of the H2O 1b(1) delocalized molecular orbital with surface wave functions.