The bound state energies of a 1-dimensional finite quantum square well (FSW) can be determined using a geometric method, involving a smooth mapping between two copies of the complex plane. The method allows one to identify particular strengths of the FSW at which the system can become unusually sensitive to changes in the well depth or geometry. In the present paper we explore that sensitivity, and exhibit a 3-D visualization of the solutions.

The amorphization and alloying behavior of an Fe-Cu system were investigated by a three-dimensional molecular dynamics simulation. A repetitive process of attachment and compression of Fe and Cu boxes was applied for modeling the mechanical milling. Metallic glass and amorphous structures formed upon compression and relaxation, respectively. Short- and medium-range orders were found by normalizing all the radial distribution function peak positions to the first peak position. The values of the compressed box agreed well with those of undercooled melts, while the relaxed box values aligned with the glassy iron value. Voronoi polyhedron analysis revealed that the fraction of crystalline structure decreased and the icosahedra-like short-range order increased upon the processes. Fe and Cu atoms became uniformly distributed, and the fraction of Fe-Cu pairs increased upon the attachment processes. The molecular dynamics simulation with the repetitive processes can reveal the processes of amorphization and mixing in the Fe-Cu system.

Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model uses a compartmental approach including dynamic and nonlinear behavior of transmission through three factors: susceptible, infected, and removed (recovered and deceased) individuals. Using the Lambert W Function, we propose a framework to study solutions of the SIR model. This demonstrates the applications of COVID-19 transmission data to model the spread of a real-world disease. Different models of disease including the SIR, SIRmp and SEIRρqr model are compared with respect to their ability to predict disease spread. Physical distancing impacts and personal protection equipment use are discussed with relevance to the COVID-19 spread.

A two-parameter model for chirping the frequency of a plane-wave laser pulse is introduced using a binomial expansion. Acceleration of single electrons, through interaction with the plane-wave binomially chirped laser pulse, is investigated by solving the relativistic equations of motion, analytically and numerically. Multi-GeV energy gains are reported from interaction with 10 $$^{20}$$ W/cm $$^2$$ peak-intensity chirped pulses.

Graphene Nanoribbons (GN), being an important class of next-generation carbon materials, are of immense interest and find innumerable applications in diverse fields. A variation of the generalized Lambert W function, called the Offset Logarithm function, has been found to have important applications in fields such as physics, engineering and nanotechnology. We study the electronic properties of zigzag GN and use the generalized Lambert W function to study the eigenvalue equations of the massless Dirac equation applied to zigzag GN. We have studied the effects of nanoribbon width and determined the parameters that significantly affect the obtained solutions.

Advances in optimizing thermoelectric material efficiency have seen a parallel activity in theoretical and computational advances. In the current work, it is shown that the calculation of exact Fermi-Dirac integrals enables the generalization of the Wiedemann-Franz law (WF) to optimize the dimensionless thermoelectric figure of merit ZT. This is done by optimizing the Seebeck coefficient, the electrical conductivity and the thermal conductivity. In the calculation of the thermal conductivity, both electronic and phononic contributions are included. The solutions provide insight into the relevant parameter space including the physical significance of complex solutions and their dependence on the scattering parameter r and the reduced chemical potential.

Airborne particulate matter (PM) pollutants were sampled from an urban background site in Sharjah, United Arab Emirates. The fine fraction (PM2.5) (particulates with aerodynamic diameters of less than 2.5 μm) was collected on 47-mm Teflon filters and analyzed using a combined set of non-destructive techniques in order to provide better understanding of the sources of pollutants and their interaction during transport in the atmosphere. These techniques included gravimetric analysis, equivalent black carbon (EBC), X-ray fluorescence, scanning electron microscopy, and X-ray diffraction. Generally, the PM2.5 concentrations are within the limits set by the World Health Organization (WHO) and the United States (US) Environmental Protection Agency. The EBC content is in the range of 10–12% of the total PM concentration (2–4 µg m−3), while S (as ammonium sulfate), Ca (as calcite, gypsum, and calcium carbonate), Si (as quartz), Fe, and Al were the major sources of PM pollution. EBC, ammonium sulfate, Zn, V, and Mn originate from anthropogenic sources such as fossil fuel burning, traffic, and industrial emissions. Natural elements such as Ca, Fe, Al, Si, and Ti are due to natural sources such as crustal materials (enhanced during dust episodes) and sea salts. The average contribution of natural sources in the total PM2.5 mass concentration over the sampling period is about 40%, and the contribution of the secondary inorganic compounds is about 27% (mainly ammonium sulfate in our case). The remaining 22% is assumed to be secondary organic compounds.

We used a multistage PIXE inertial impactor with nine different aerodynamic diameter ranges (between 16 and 0.06 μm) to sample indoor particulate matter (PM). X‐ray fluorescence (XRF) measurements performed at cutoff diameters (CoDs) of 0.25, 0.5, 1, 2, 4, and 8 μm were used to identify elements in various size fractions. Anthropogenic sources were the dominant sources for fine and ultrafine particle sizes. The XRF results show that natural sources also contribute to the fine and ultrafine fractions of pollutants. Scanning electron microscopy and energy‐dispersive system analysis were performed on membranes having PM CoDs of 4, 2, 1, 0.5, and 0.25 μm. Elemental mappings show the membranes with PM of CoDs 0.25 and 0.5 μm having S as a dominant element, confirming the results obtained with XRF. Strong correlation among maps of S, N, and O show that ammonium sulfate is the major constituent at these size fractions. Other elements such as Si, Ca, Fe, Al, and Mg show up in smaller amounts at these size fractions but increase for membranes with larger particles. For size fractions larger than 0.5 μm, there is a good correlation between the elemental maps of these elements and oxygen, indicating that these elements exist mostly in oxide forms. The absence of clear N signals and the correlation between the Ca and S maps indicate that S in these size fractions is not due to ammonium sulfate. The presence of Mg, K, Cl, and Na at these CoDs shows that these elements are due to salts originating from sea breeze.

An urban background sampling campaign was performed to measure PM2.5 pollutants in Sharjah, United Arab Emirates.Gravimetric analysis, smoke stain reflectometry, XRF and XRD measurements and analysis were performed on samples collected on 47 mm Teflon filters following international sampling procedures.The PM2.5 amounts are within WHO limits in the absence of natural dust storms.Elemental composition and phase identification of major pollutants were determined.In the absence of dust storms, fossil fuel burning originating from traffic and energy generation are the major sources of PM2.5 in the form of secondary phases formed from gaseous precursors.Primary pollutants such as quartz, calcite and gypsum and sea salts are the main pollutants during dusty days.Natural sources such as sea salts and crustal materials also contribute to PM2.5 both as primary sources and through interaction with anthropogenic emissions to form new secondary phases depending on factors such as the ambient conditions and primary pollutants.Integration of different techniques provided us with a better understanding of sources of pollutants and their interaction during their transport in the atmosphere.Reduction of major secondary pollutants in PM2.5 has already been observed through various clean energy initiatives in the country and by implementing green building codes and enforcing strict regulations on industrial emissions.

A double stage, low volume particle sampler was used to collect PM10 and PM2.5 aerosol particles, both indoor and outdoor. XRF, SEM/EDS, Micro-Raman and XRD techniques were used to identify both the elemental composition and chemical speciation of particulate matter (PM) of both size fractions. The integration of the above techniques has enabled us to identify the constituents of both the coarse and fine fractions of PM. We have also found that the large amounts of ammonium sulfates ((NH4)2SO4) form in the atmosphere as a result of interaction of natural (coarse) fraction of pollutants with anthropogenic emissions such as SO2, NOx, ammonia(NH3) and ammonium compounds, originating from fossil fuel burning mainly for energy generation. Such interactions of PM during transport in the atmosphere, in the presence of humidity, also modify the properties and toxicity of PM, especially for the fine and ultra-fine fractions. EDS elemental maps, XRD and RAMAN spectroscopy have enabled us to identify several secondary pollutants that form in the atmosphere as a result of such interactions, such as (CaMg(CO)3) and ((Fe,Mg)2SiO4). Anthropogenic emissions therefore have drastic consequences in forming new compounds with fine particulate sizes as a result of interaction with natural coarse emissions originating from dust storms, sea salts and crustal materials. These secondary fine pollutants may have severe health consequences. Our results suggest that reducing emissions of power plants will drastically reduce these undesired reactions and the formation of these fine-sized secondary pollutants. Moving towards renewable and clean energy sources such as solar and nuclear sources will lead to reducing secondary pollutants emissions. The UAE has recently initiated several projects both related to both solar and nuclear power plants. These projects will lead to tremendous reduction of fine particulate pollutants originating from primary anthropogenic sources and from interaction of natural coarse pollutants with these anthropogenic emissions.

Alkaline-earth beryllium and magnesium oxides are fundamental materials in nuclear industry and thermal neutron scattering applications. The calculation of the thermal neutron scattering cross sections requires a detailed knowledge of the lattice dynamics of the scattering medium. The vibrational properties of BeO and MgO are studied using first-principles calculations within the frame work of the density functional perturbation theory. Excellent agreement between the calculated phonon dispersion relations and the experimental data have been obtained. The phonon densities of states are utilized to calculate the scattering laws using the incoherent approximation. For BeO, there are concerns about the accuracy of the phonon density of states used to generate the current ENDF/B-VII.1 libraries. These concerns are identified, and their influences on the scattering law and inelastic scattering cross section are analyzed. For MgO, no up to date thermal neutron scattering cross section ENDF library is available, and our results represent a potential one for use in different applications. Moreover, the Be and MgO efficiencies as neutron filters at different temperatures are investigated. BeO is found to be a better filter than MgO, especially when cooled down, and cooling MgO below 77 K does not significantly improve the filter's efficiency. (C) 2015 Elsevier Ltd. All rights reserved.

Theoretical investigations are presented, and their results are discussed, of the laser acceleration of a single electron by a chirped pulse. Fields of the pulse are modeled by simple plane-wave oscillations and a cos(2) envelope. The dynamics emerge from analytic and numerical solutions to the relativistic Lorentz-Newton equations of motion of the electron in the fields of the pulse. All simulations have been carried out by independent Mathematica and Python codes, with identical results. Configurations of acceleration from a position of rest as well as from injection, axially and sideways, at initial relativistic speeds are studied.

Single MeV electrons in vacuum subjected to single high-intensity quadratically chirped laser pulses are shown to gain multi-GeV energies. The laser pulses are modelled by finite-duration trapezoidal and cos(2) pulse-shapes and the equations of motion are solved numerically. It is found that, typically, the maximum energy gain from interaction with a quadratic chirp is about half of what would be gained from a linear chirp.

Synchrotron-based, high-energy X-ray diffraction measurements are used to study the local strain fields underlying the transient fatigue crack growth rate retardation produced by a single overload cycle known as the overload effect. Specifically, 4140 steel compact tension specimens fatigued for varying levels of crack growth after an overload cycle have been studied with in-situ diffraction under varying external loads. The load responses of the strain at the overload-position, versus at the crack tip, are focused upon in detail. The large compressive residual strain at the overload-point is observed to remain essentially unchanged even after the overload-point is left in the wake of the propagating crack tip. The differential strain-load response at the crack-tip/overload position before and immediately after the overload is seen to be unchanged. Once the overload point is behind the crack tip, a highly nonlinear behavior is observed in which the load response of the strain field transfers from the overload -point to the crack tip when the load exceeds a critical value. The results are discussed in terms of plasticity-induced crack face contact at the overload point as an important local mechanism contributing to the “overload effect” in this specific system.

The feasibility of using energy dispersive X-ray diffraction to characterize full size battery cells is demonstrated by unprecedented in situ measurements of the electrochemical processes taking place inside high temperature sodium metal halide (Na/MCl2, M = Ni and/or Fe) cells during charge/discharge cycling. Diffraction data provide phase information either via line scans across the 5 cm wide cells or via fixed location scans as a function of time. The data confirm the propagation of a well-defined chemical reaction front, as a function of charge/discharge time, beginning at the ceramic separator and proceeding inward. Measurement of the temporal evolution of the phase abundances yields mechanistic understanding and reaction rates as a function of charge/discharge state. In the case where M includes Fe, the data also clearly show the appearance of an intermediate phase, Na6FeCl8, during charging, thereby underscoring the power of this technique to reveal subtle mechanistic information. A number of additional detailed electrochemical kinetic effects are also discussed. This study shows that in situ high energy X-ray diffraction characterization of advanced battery cells in space and time is eminently feasible on a routine basis, and has great potential to advance the understanding of "buried" chemical processes.

Processing of YBa2Cu3O6+x superconducting samples by employing different precursor powder preparation techniques such as ball milling, attrition milling and also narrow particle size distribution powder preparation through coprecipitation by spraying will be discussed. CuO coated with oxalates shows the lowest resistance above T up to room temperature. The extent of corrosion by water has been studied by employing magnetic susceptibility, XPS and X-ray diffraction. Superconducting samples are affected to a considerable extent when treated in water at 60° C and the severity of the attack increases with time.

The feasibility of using energy dispersive X-ray diffraction to characterize full size battery cells is demonstrated by unprecedented in situ measurements of the electrochemical processes taking place inside high temperature sodium metal halide (Na/MCl2, M = Ni and/or Fe) cells during charge/discharge cycling. Diffraction data provide phase information either via line scans across the 5 cm wide cells or via fixed location scans as a function of time. The data confirm the propagation of a well-defined chemical reaction front, as a function of charge/discharge time, beginning at the ceramic separator and proceeding inward. n situ X-ray diffraction Measurement of the temporal evolution of the phase abundances yields mechanistic understanding and reaction rates as a function of charge/discharge state. In the case where M includes Fe, the data also clearly show the appearance of an intermediate phase, Na6FeCl8, during charging, thereby underscoring the power of this technique to reveal subtle mechanistic information. A number of additional detailed electrochemical kinetic effects are also discussed. This study shows that in situ high energy X-ray diffrac-