UV light at 222 nm inactivates SARS-CoV-2 virions at intensities appearing to be benign to skin and eyes. It can disinfect air without requiring protection of persons from UV as is needed at longer UV wavelengths. The lower risk of damage from 222-nm UV results from enhanced absorption of this UV in the outermost parts of eyes and skin. Microbes can be partially shielded from 250- to 285-nm UV when in host particles. Does the higher absorption at 222-nm increase the shielding of microbes within particles, and if so, to what extent? We use literature values to approximate the compositions and optical properties of SARS-CoV-2 virions and four types of fluids from the respiratory tract and mouth. We model virions within spherical host particles (homogeneous except for the virions), calculate the UV absorbed by the virions, and use these values to calculate survival fractions of virions in particles (Sp). We find that shielding is relatively small for particles generated in quiet breathing (typically 1.5-mu m or smaller). For larger particles, shielding increases as the host-particle diameter increases. Shielding is greater at 222- than at 254-nm for all pairs of UV-fluence and particle-diameters calculated. The higher eye-safety thresholds at 222-nm allow use of larger fluences and shorter inactivation times. Because shielding increases as host-particle size increases, and because significant fractions of airborne disease-transmitting particles have diameter >1.5-mu m, it appears that the sizes and optical properties of host particles must be considered in designing and verifying UV inactivation systems for such particles.

Abstract Germicidal ultraviolet light (GUV) is routinely used to kill pathogenic bacteria and viruses for limiting the transmission of disease. Microbes such as bacterial spores can form aggregates either with themselves or other particles. These aggregates can shield organisms within them from GUV and thus make it difficult to achieve a desired reduction in viability. There is a need to better understand shielding of microbes from UV, and how it depends upon particle size and composition. To determine the survival fractions of spores in clusters (S p) we aerosolized Bacillus anthracis Sterne spores, collected the clusters onto a surface, illuminated the samples with the desired fluence (J/m2) of 254-nm GUV, then resuspended the spores, plated serial dilutions and counted live colonies. The S p was calculated for each time point using the culturable organisms in the exposed and unexposed samples. We also modeled the S p of spores in clusters on a surface in air. In these mathematical models, each spore was approximated as a homogenous sphere having optical properties approximating those of spores. The absorption of GUV by each sphere within the cluster resting on a surface was calculated using the Multi-Sphere T-Matrix (MSTM). Plots showing both measured and calculated S p versus GUV fluence illustrate similarities between measured and calculated values and increases in S p with cluster size. These studies add to the evidence that particle sizes need to be considered when modeling, designing, and using GUV systems to reduce spreading of infectious disease. The potential relevance to 222-nm GUV inactivation is discussed. Graphical Abstract

The mathematical concepts and procedures associated with calculating the scattered field from a particle of arbitrary shape and composition, when excited by an incident field of arbitrary form, are presented. The general analytical forms of the incident and scattered fields, and the matrix relationship relating the two fields for a given particle, are introduced. Common analytical and numerical methods for the calculation of the T matrix are discussed for particles of nonspherical shape and/or inhomogeneous composition.

Ultraviolet (UV) germicidal irradiation (UVGI) is used to inactivate viruses and kill other microbes to de-crease transmission of disease. Microbes such as bacterial spores can occur within clusters of spores or other particles. Such particles, in air or in water, can in some cases partially shield spores within them from UVGI, whether on a surface or suspended. There is a need to better understand how such shielding varies with particle size, composition, and illumination angle. Here the Multi-Sphere T-Matrix (MSTM) method is used to model the absorption of UVGI by bacterial spores in clusters, where each spore is approximated as a homogeneous sphere. The clusters of spores may be surrounded only by air or may be within an encompassing "host" sphere in air. Calculated results of the UV absorption efficiencies for each spore are illustrated for clusters of 54 spores within host spheres of different optical properties, on surfaces with different compositions (polycarbonate, iron and aluminum), and for illumination with UV light from different directions with respect to the cluster and the surface. For the solar UV wavelengths 302 and 325 nm and the deep purple 450 nm, and the unpigmented bacteria modeled here, the pene-tration depths in both the spores and host sphere are so much larger than the cluster and host sphere size (5.08 mu m) that the general effect on the absorption by spores is relatively insensitive to wavelength. Results at 266 nm suggest that in using and validating UVGI for inactivation, the sizes and compositions of the particles are important. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

An extension of the parameter space available to the Multiple Sphere T Matrix (MSTM) code is described. The code can now calculate electromagnetic scattering and absorption characteristics of multiple spheres that are placed adjacent to multiple plane boundaries perpendicular to the z direction, with each boundary separating layers of different complex refractive index. The spheres can also form infinitely periodic structures in the x -y plane. The code retains all previous features, such as the spheres being comprised of optically active materials and having positions internal or external to other spheres. Example calculations are presented to demonstrate the veracity of the code. (C) 2022 Elsevier Ltd. All rights reserved.

The application of an algorithm, based upon an FFT-enabled discrete Fourier convolution, to the multiple sphere superposition solution is presented. As opposed to the N-S(2) operation count scaling for the standard superposition solution algorithm, where N-S is the number of spheres, the accelerated algorithm results in closer to N-S ln N-S scaling. The new algorithm has been adopted into the Multiple Sphere T Matrix (MSTM) fortran-90 code, and the code has been optimized to allow for rapid calculation of configuration-and/or orientation-averaged radiative properties of large-scale systems of randomly-positioned spheres. Improvement in computational times by more than two orders of magnitude are possible for systems containing in excess of 1000 spheres. Illustrative examples of the application of the updated code are presented. (C) 2022 Elsevier Ltd. All rights reserved.

ABSTRACT SARS-CoV-2 and other microbes within aerosol particles can be partially shielded from UV radiation. The particles refract and absorb light, and thereby reduce the UV intensity at various locations within the particle. Shielding has been demonstrated in calculations of UV intensities within spherical approximations of SARS-CoV-2 virions that are within spherical particles approximating dried-to-equilibrium respiratory fluids. The purpose of this paper is to calculate the survival fractions of virions (i.e., the fractions of virions that can infect cells) within spherical particles approximating dried respiratory fluids, and to investigate the implications of these calculations for using UV light for disinfection. The particles may be on a surface or in air. In this paper the survival fraction ( S ) of a set of virions illuminated with a UV fluence ( F , in J/m 2 ) is approximated as S= exp( -kF) , where k is the UV inactivation rate constant (m 2 /J). The average survival fractions ( S p ) of all the simulated virions in a particle are calculated using the calculated decreases in fluence. The results show that virions in particles of dried respiratory fluids can have significantly larger S p than do individual virions. For individual virions, and virions in 1-, 5-, and 9-µm particles illuminated (normal incidence) on a surface with 260-nm UV light, the S p = 0.00005, 0.0155, 0.22 and 0.28, respectively, when kF= 10. The S p decrease to <10 −7 , <10 −7 , 0.077 and 0.15, respectively, for kF =100. Calculated results also show that illuminating particles with UV beams from widely separated directions can strongly reduce the S p . These results suggest that the size distributions and optical properties of the dried particles of virion-containing respiratory fluids are likely important in effectively designing and using UV germicidal irradiation systems for microbes in particles. The results suggest the use of reflective surfaces to increase the angles of illumination and decrease the S p . The results suggest the need for measurements of the S p of SARS-CoV-2 in particles having compositions and sizes relevant to the modes of disease transmission.

UV radiation can inactivate viruses such as SARS-CoV-2. However, designing effective UV germicidal irradiation (UVGI) systems can be difficult because the effects of dried respiratory droplets and other fomites on UV light intensities are poorly understood. Numerical modeling of UV intensities inside virus-containing particles on surfaces can increase understanding of these possible reductions in UV intensity. We model UV intensities within spherical approximations of virions randomly positioned within spherical particles. The model virions and dried particles have sizes and optical properties to approximate SARS-CoV-2 and dried particles formed from respiratory droplets, respectively. In 1-, 5- and 9-µm diameter particles on a surface, illuminated by 260-nm UV light from a direction perpendicular to the surface, 0%, 10% and 18% (respectively) of simulated virions are exposed to intensities less than 1/100th of intensities in individually exposed virions (i.e., they are partially shielded). Even for 302-nm light (simulating sunlight), where absorption is small, 0% and 11% of virions in 1- and 9-µm particles have exposures 1/100th those of individually exposed virions. Shielding is small to negligible in sub-micron particles. Results show that shielding of virions in a particle can be reduced by illuminating a particle either from multiple widely separated incident directions, or by illuminating a particle rotating in air for a time sufficient to rotate through enough orientations. Because highly UV-reflective paints and surfaces can increase the angular ranges of illumination and the intensities within particles, they appear likely to be useful for reducing shielding of virions embedded within particles.

To observe and study the effects of the volume packing density on polarimetric scattering by deposited particulate materials, a comparison is made between the vector radiative transport equation (VRTE) and the plane wave plane parallel (PWPP) models for the polarized bidirectional reflectance and transmittance from plane parallel layers of randomly distributed, wavelength-sized particles. Calculations have been performed on ice and mineral materials with refractive indices of m = 1.31 and m = 1.5 + 0.01i respectively. In these simulations, particle volume fraction ranges from around 0.05-0.3 for deposits consisting of spherical particles with size parameters of one and two. It is found that the PWPP model results converge to those predicted by the VRTE at small (similar to 5% or less) particle volume fractions. At higher volume fractions, the difference between the PWPP and VRTE results depends strongly on the particle size and refractive index, yet not so much on the optical thickness (equivalently, volume of particles per unit area of layer). PWPP simulation results of coherent backscattering effects - brightness opposition and polarization opposition effects - for ice and mineral particles are also represented. Their dependency on the particle volume fraction and particle size has been discussed. (C) 2018 Published by Elsevier Ltd.

We apply machine-learning algorithms to the calculated light-scattering patterns from particles having seven different common and naturally occurring shapes to assess the accuracy of shape classification based on light scattering. We consider different input data sets including one- and two-dimensional scattering functions of both intensity and polarization. Our scattering data set is produced from particles of volume-equivalent size parameter 5, and refractive index m = 1.5 + Oi. As expected, classification capabilities were much greater when the two-dimensional scattering data were used than when only one-dimensional data were considered. When the two-dimensional intensity patterns are considered, classification accuracies were approximately 70% for the regularly shaped particles and above 90% for the highly irregularly shaped particles. These capabilities increased slightly when linear polarization was used as input. Although all our results are specific to our particular data set, machine-learning techniques are easily generalizable. This exercise suggests that particle discrimination can be achieved in practical experiments using light-scattering patterns through deep learning. (C) 2019 Elsevier Ltd. All rights reserved.

A formulation is developed for numerically solving the frequency domain Maxwell's equations in plane parallel layers of inhomogeneous media. As was done in a recent work [1], the plane parallel layer is modeled as an infinite square lattice of W x W x H unit cells, with W being a sample width of the layer and H the layer thickness. As opposed to the 3D volume integral discrete dipole formulation, the derivation begins with a Fourier expansion of the electric field amplitude in the lateral plane, and leads to a coupled system of 1D ordinary differential equations in the depth direction of the layer. A 1D dyadic Green's function is derived for this system and used to construct a set of coupled 1D integral equations for the field expansion coefficients. The resulting mathematical formulation is considerably simpler and more compact than that derived, for the same system, using the discrete dipole approximation applied to the periodic plane lattice. Furthermore, the fundamental property variable appearing in the formulation is the Fourier transformed complex permittivity distribution in the unit cell, and the method obviates any need to define or calculate a dipole polarizability. Although designed primarily for random media calculations, the method is also capable of predicting the single scattering properties of individual particles; comparisons are presented to demonstrate that the method can accurately reproduce, at scattering angles not too close to 90, the polarimetric scattering properties of single and multiple spheres. The derivation of the dyadic Green's function allows for an analytical preconditioning of the equations, and it is shown that this can result in significantly accelerated solution times when applied to densely-packed systems of particles. Calculation results demonstrate that the method, when applied to inhomogeneous media, can predict coherent backscattering and polarization opposition effects. (C) 2018 Elsevier Ltd. All rights reserved.

Recent in-situ studies of the environment of comet 67P/Churyumov-Gerasimenko by the dust instruments onboard the Rosetta spacecraft have indicated a complex structure of cometary dust particles. The majority of those particles appeared to be large aggregates of hierarchical structure, i.e. aggregates of particles, which, in turn, were aggregates of smaller particles. This confirmed an earlier hypothesis that dust particles in protoplanetary disks grow under hierarchical growth process. Thus, it is very likely that hierarchical aggregates are common type of natural dust particles. In this paper, we present results of computer simulations of light scattering by a variety of hierarchical aggregates to determine how their structure affects their brightness and polarization phase curves as well as photometric and polarimetric color, and albedo. The computations were done using Multi-Sphere T-Matrix method. Our results show that the type of hierarchical structure of aggregates, specified by the number of particles at each level of hierarchy, causes variations in their light-scattering characteristics, which noticeably exceed the variations caused by different configuration of monomers in the aggregates of the same hierarchical structure. Although we could not find any regularities in the brightness and polarization dependence on the structure of the aggregates, our results clearly show that not only composition or size of aggregates, but also their specific structure should be carefully examined when light scattering by cometary or any other type of dust is modeled. Specifically, we may need to reconsider modeling the cometary dust particles using simple ballistic particle-cluster and cluster-cluster aggregates. (C) 2017 Elsevier Ltd. All rights reserved.

Two methods for computing the normal incidence absorptance and hemispherical reflectance from plane parallel layers of wavelength–sized spherical particles are presented. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a system of randomly–positioned spherical particles excited by an incident plane wave. The second method is based upon the scalar radiative transport equation (RTE) applied to a plane parallel medium. Comparisons are made using five values of particle refractive index, sphere size parameters ranging from 1 to 4, and particle volume concentrations ranging from 0.05 to 0.4. The results indicate that the multiple sphere T matrix method (MSTM) and RTE predictions of hemispherical reflectance and absorptance converge when particle volume fraction becomes small. At higher volume fractions the RTE can yield results for hemispherical reflectance that, depending on the particle size and refractive index, significantly depart from the exact predictions. On the other hand, RTE and MSTM predictions of absorptance have a much closer agreement which is largely independent of the sphere optical properties and volume concentration.