In the realm of light scattering computational techniques, the T-matrix method serves as a pivotal tool for analysing dust particles composed of aggregated spherical monomers. However, an inherent and significant limitation restricts its application to small aggregates due to the computational demands of processing the translation matrix, whose size becomes prohibitive for aggregates with a large number of spheres. The Mean-Field T-matrix method (MFTM) was proposed as an approximation to address this issue, enabling the treatment of arbitrarily large particles. In the present study, the MFTM method is extended to encompass dust particles that are large, irregular aggregates of polydisperse spherical monomers made from various materials. Additionally, a recently proposed accurate pair correlation function is integrated to describe the spatial distribution of monomers within the aggregate. These advancements render the refined MFTM method both efficient and capable of processing realistic, large dust aggregates. This paper presents a comprehensive application of the enhanced MFTM method to fractal aggregates of spheres with radii following a Schulz distribution. Notably, the refined method is expected to facilitate the derivation of optical properties of atmospheric aerosols and the interpretation of observations from protoplanetary disks.

The pair correlation function, g(r), is a fundamental descriptor of the inner structure of fractal aggregates of monomers. It provides a natural tool for studying physical properties involving two-point interaction (e.g. optics of aggregates). Several domains of distances between pairs of monomers have been identified. The fractal domain (in which g(r) is a power-law) is generally dominant for large aggregates. We show here that the local behavior of g(r)-involving monomers tangent to a given monomer-is necessary for most of the quantitative applications, even if that local domain is not directly related to fractal morphology. We derive a simple generic pair correlation function for fractal aggregates, depending on three structural parameters only: the fractal dimension, d(f) ; the prefactor, k(f) ; the local mean coordination number, (Z) over bar. Unlike the fractal dimension, the prefactor and the mean coordination number are not universal since they depend on many parameters of the generation process. We discuss the impact of the definite shape of g(r) on the aggregate structure factor profile (a measurable quantity through small-angle x-ray scattering). Improvement from the new g(r) shape is also illustrated deriving an analytical expression of the geometric cross section, G, of aggregates for fractal dimension <2 . Accuracy is checked by comparing with numerical data from aggregates of fractal dimension d(f) = 1.9 . On the up-to-date analytical expression of G, the contributions of the short- and long-range behaviours of g(r) are well separated, and it is clear that the local behavior of the pair correlation function is required to obtain accurate values of the geometric cross section. Thus, in addition to the fractal structure of aggregates, the local structure of aggregates (to which the prefactor k(f) and the g(r) divergence at short distances are related) also appears important to accurately describe their physical features.

Aggregated particles and aerosols are common in natural or industrial environments. Analysing their scattering and absorption properties with precise methods may prove useful for gaining information about real particles, using remote sensing or in situ active optical instruments in natural environments. Many methods, with varying complexities, were developed in the past. For aggregates of spheres, the most recent version of the T-Matrix method by Mackowski and Mishchenko (2011) is able to treat the problem almost exactly and can yield all the details of the scattering properties. However, for computational reasons, the T-Matrix method cannot handle large particles. In order to deal with large particles, a mean-field version of the T-Matrix theory was developed by Botet et al. (1997) for aggregates of identical spheres and used in particular to analyse the case of Titan haze. This mean-field T-Matrix method is efficient to quickly calculate accurate approximations of many optical properties of aggregates of Mie spheres, but it is inherently limited by the mean field approximations. It uses crude approximation of the pair-correlation functions (Seignovert et al., 2017) and leads to inaccurate estimations in the geometrical optics limit (Tazaki and Tanaka, 2018). In the present work, we bring improvements that overcome these two limitations. This significantly increases the validity range of the method and its accuracy. We display comparisons with the results obtained with T-Matrix method in order to assess the performance of the new version of the mean field method (MFT-M+).

Numerical analogues of non-fractal porous cometary dust particles are generated using a recently introduced model of open-pore solid particles. The refractive index of amorphous silicate is considered and the particle sizes follow a Sekanina-Hanner distribution within the size-range (0.01μm-1μm). Using the Discrete Dipole Approximation (DDA) method, we calculate the thermal re-emission spectrum of a population of porous particles in the spectral region 0.2–39.8 μm and the equilibrium temperature of the particles (when placed at 1 AU distance from Sun). Porosity tends to reduce the temperature of the particles because porous particles radiate heat more effectively than dense particles. A characteristic particle size is determined for which the particle temperature is maximum regardless of the porosity. The temperature of a cloud of polydisperse particles is more homogeneous for highly porous particles. These results are compared with those generated by Mie theory where the Bruggeman mixing rule is applied (EMT method). When agreement between the DDA and the EMT results is achieved, simple approximations are derived from the EMT to analyze and make clear the various behaviors of the spectral thermal re-emission revealed in the numerical data. In particular, the reason why the emission peak around 10μm is depressed by porosity and shifted to the smaller wavelength by a steeper particle-size distribution is explained.

Spatial structures of electromagnetic near-fields generated by plasmonic resonances are studied through numerical simulations. Resonances can appear in silver nanoplates onto which nanoparticles of various shapes are deposited. For forthcoming biophysical applications, nanoparticles are considered here as irregular aggregates of grains made of DNA material. The Discrete Dipole Approximation technique is used to calculate the electromagnetic field profiles. In certain controlled physical situations, the plasmonic pattern appears to be the glowing anti-shadow of the deposited nanoparticle, and such a pattern locally produces strong increase in the electromagnetic fields. Even when the nanoparticle size is much smaller than the wavelength, fine (sub-wavelength) details of the anti-shadow are directly related to the shape of the nanoparticle. These observations should result in a better understanding of the Surface-Enhanced Raman Scattering process and an improvement in nanocharacterization techniques.

Completing a Swiss-cheese theorem of Lieb and Lebowitz (LL), we prove that any population of spheres with power-law radius distribution ∝ 1 / r d f + 1 can completely fill 3D Euclidean space if the exponent is such that 2.8 ⩽ d f < 3. This sufficient condition extends considerably the known part of the ensemble of space-filling populations of polydisperse spheres. The self-similar spatial arrangement of the polydisperse spheres related to the theorem is discussed using a numerical example with d f = 2.875. By calculating the small-angle scattering structure factor of the resulting packing, we found it to present several crystalline peaks indicating some regularity. This is significantly different from the featureless structure factor of an Apollonian packing which represents total disorder. We thereby argue that the LL algorithm for filling space with spheres is fundamentally different from Apollonian constructions.

Aluminium salts such as aluminium chlorohydrate (ACH) are the active ingredients of antiperspirant products. Their mechanism of action involves a temporary and superficial plugging of eccrine sweat pores at the skin surface. We developed a microfluidic system that allows the real time observation of the interactions between sweat and ACH in conditions mimicking physiological sweat flow and pore dimensions. Using artificial sweat containing bovine serum albumin as a model protein, we performed experiments under flowing conditions to demonstrate that pore clogging results from the aggregation of proteins by aluminium polycations at specific location in the sweat pore. Combining microfluidic experiments, confocal microscopy and numerical models helps to better understand the physical chemistry and mechanisms involved in pore plugging. The results show that plugging starts from the walls of sweat pores before expanding into the centre of the channel. The simulations aid in explaining the influence of ACH concentration as well as the impact of flow conditions on the localization of the plug. Altogether, these results outline the potential of both microfluidic confocal observations and numerical simulations at the single sweat pore level to understand why aluminium polycations are so efficient for sweat channel plugging.

Are aluminium ions unavoidable in antiperspirants? To answer this question, we present confocal microscopy images of dendritic plugs appearing in sweat flowing across a microfluidic channel in the presence of aluminium salts. By comparing with numerical simulations, we identify the mechanisms forming this structured protein gel inside the pore.

Measuring the structure factor, S(q), of a dispersion of particles by Small-Angle X-ray Scattering provides a unique method to investigate the spatial arrangement of colloidal particles. However, it is impossible to find the exact location of the particles from S(q) because some information is inherently lacking in the SAXS signal. The two standard ways to analyse an experimental structure factor are then to compare it either to structure factors computed from simulated systems, or to analytical structure factors calculated from approximated systems. For liquids of monodisperse hard spheres, the latter method provides analytical structure factors through the Ornstein-Zernike equation used with the Percus-Yevick closure equation. The structure factors obtained in this way were not adequate for the more common dispersions of polydisperse particles. However, Vrij, Bloom and Stell were able to demonstrate that the same mathematical framework could be extended to yield accurate approximations for the experimental structure factor. Still, this solution has remained underused because of its mathematical complexity. In the present work, we derive and report the complete Percus-Yevick solution for general polydisperse hard-spheres systems in a concise form that is straightforward to use. The form of the solution is made simple enough to give ready solutions of several important particle-radius distributions (Schulz, truncated normal and inverse Gaussian). We also discuss in detail the case of the power-law radius distribution, relevant in the case of systems made of an Apollonian packing of spheres, as recently discovered experimentally in high internal-phase-ratio emulsions.

Monte Carlo simulations, fully constrained by experimental parameters, are found to agree well with a measured phase diagram of aqueous dispersions of nanoparticles with a moderate size polydispersity over a broad range of salt concentrations, c_{s}, and volume fractions, ϕ. Upon increasing ϕ, the colloids freeze first into coexisting compact solids then into a body centered cubic phase (bcc) before they melt into a glass forming liquid. The surprising stability of the bcc solid at high ϕ and c_{s} is explained by the interaction (charge) polydispersity and vibrational entropy.

We have discovered the existence of polydisperse high internal-phase-ratio emulsions (HIPE) in which the internal-phase droplets, present at 95% volume fraction, remain spherical and organise themselves according to Apollonian packing rules. These polydisperse HIPEs are formed by emulsifying oil dropwise in a surfactant-poor aqueous continuous phase. After stirring has ceased, their droplet size distributions begin to evolve spontaneously and continuously through coalescence towards well-defined power laws with the Apollonian exponent. Small-angle X-ray Scattering performed on aged HIPEs demonstrate that the droplet packing structure agrees with that of a numerically simulated random Apollonian packing. We argue that when such concentrated emulsions are allowed to evolve, the coalescing droplets must obey volume and sphericity conservation. This leads to a mechanism that differs from typical coalescence in dilute emulsions.

We have discovered the existence of extremely polydisperse High Internal-Phase-Ratio Emulsions (HIPEs) in which the internal-phase droplets, present at 95% volume fraction, remain spherical and organize themselves in the available space according to Apollonian packing rules. Such Apollonian emulsions are obtained from dispersing oil dropwise in water in the presence of very little surfactant, and allowing them to evolve at rest for at least a week. The packing structure of the droplets was confirmed through size distribution measurements that evolved spontaneously towards power laws with the known Apollonian exponents, as well as comparison of the structure factors of aged HIPEs measured by Small-Angle X-ray Scattering with that of a numerically simulated Random Apollonian Packing. Thanks to the perfect sphericity of the droplets, Apollonian emulsions were found to display Newtonian flow even at such extremely high volume fraction. We argue that these fascinating space-filling assemblies of spherical droplets are a result of coalescence and fragmentation processes obeying simple geometrical rules of conserving total volume and sphericity, and minimizing the elastic energy associated with interactions of neighbouring droplets.

In the present work, we propose a comparative study of optical properties in the visual spectral regime of porous dust particles having porosities ranging from 0% (compact particle) to 50% (as much matter as void in a same particle), generated using two different models considering particle as an ensemble of dipoles much smaller than wavelength. One of the models (the touching-dipoles model, named below: "TD model") considers a homogeneous structure made up of touching dipoles (that is neighbouring); the dipoles are removed randomly one by one from a compact structure in such a way that the remaining structure is left connected. The other model (the non-touching-dipoles model, named below:"non-TD model") generates porous particles by randomly removing dipoles without constraining the ensemble of dipoles to remain connected. The computations of the optical properties of these disordered particles are performed using Discrete Dipole Approximation (DDA) code. Linear polarization profiles and color (i.e. the ratio between the intensities of the light scattered by particles in the comet at 0.485 mu m and 0.684 mu m wavelengths expressed in log scale) curves are shown vs. the scattering angle, and compared for the two models at different porosities. The variation of scattering efficiency factor as a function of the size parameter (X) is also studied to point out sensitivity of light scattering to different pore structures (shape and size), comparing data from particles of same porosity but generated through different processes. The results are compared with Mie results where the effective refractive index for each porosity is calculated using Bruggemann mixing rule. It is observed that light scattering properties of the TD model is not much different from the EMT-Mie model, but the non-TD model differs significantly. These difference could be due to the fact that non-TD model contains a higher number of non-Rayleigh inclusions, as compared to the TD model.

Comet 67P/Churyumov-Gerasimenko (hereafter, 67P) was observed on 2015 December 12, from 2m Himalayan Chandra Telescope in India in photometry to study its dust properties, using Bessell R and I filters. We study the photometric images to highlight coma structures and jets. The radial decrease in intensity in the different coma structures is compared to the azimuthally integrated intensities. The observations of the slopes show a quasi-steady-state coma to an optocentric distance of about km. The change in the slopes in the structures indicates changing properties of the dust particles and/or change in their local size distributions. Comparison of the radial decrease in the two wavelengths suggests a change in the local colour index. Based on the absolute photometry carried out in this work, we calculate the reddening of the comet dust that helps to characterize variations in the size and the materials of the particles. The colour index is calculated for different apertures and regions in the coma (0.40 +/- 0.07 mag) for a 22000 diameter aperture. A colour map is constructed showing the variation of the colour index through the coma. Changes appear at the transition between the coma and the tail with a low colour index (<0.3 mag) close to the optocentre and further away increasing up in the tail direction (about 0.45 mag at km). We interpret these changes in terms of dust properties and we compare our results to other remote observations of 67P including in situ Rosetta observations.

We show that the equations for the dynamics of a non-Hermitian two-state quantum system are the same as the equations of motion for a massless charged particle in an electromagnetic field. Using simple analytical arguments to prove this unexpected duality between two very different domains in physics, we further exemplify it through a case-study of polarization of light propagating in a dichroic medium with magneto-optic activity.

Context. Cometary dust particles are remnants of the primordial accretion of refractory material that occurred during the initial formation stages of the solar system. Understanding their physical structure can help constrain their accretion process. Aims. The in situ study of dust particles that were collected at slow speeds by instruments on board the Rosetta space mission, including GIADA, MIDAS, and COSIMA, can be used to infer the physical properties, size distribution, and typologies of the dust. Methods. We have developed a simple numerical simulation of aggregate impact flattening to interpret the properties of particles collected by COSIMA. The aspect ratios of flattened particles from simulations and observations are compared to distinguish between initial families of aggregates that are characterized by different fractal dimensions D f . This dimension can differentiate between certain growth modes: the diffusion limited cluster–cluster aggregates (DLCA, D f ≈ 1.8), diffusion limited particle–cluster aggregates (DLPA, D f ≈ 2.5), reaction limited cluster–cluster aggregates (RLCA, D f ≈ 2.1), and reaction limited particle–cluster aggregates (RLPA, D f ≈ 3.0). Results. The diversity of aspect ratios measured by COSIMA is consistent with either two families of aggregates with different initial D f (a family of compact aggregates with D f close to 2.5–3 and some fluffier aggregates with D f ≈ 2) or aggregates formed by a single type of aggregation process, such as DLPA. In that case, the cohesive strength of the dust particles must span a wide range to explain the range of aspect ratios observed by COSIMA. Furthermore, variations in cohesive strength and velocity may play a role in the detected higher aspect ratio range (>0.3). Conclusions. Our work allows us to explain the particle morphologies observed by COSIMA and those generated by laboratory experiments in a consistent framework. Taking into account all observations from the three dust instruments on board Rosetta, we favor an interpretation of our simulations based on two different families of dust particles with significantly distinct fractal dimensions that are ejected from the cometary nucleus.

The Rosetta space mission included three main instruments for solid dust particle analysis. The combined microscope and mass spectrometer COSIMA (Cometary Secondary Ion Mass Analyser) [1], the atomic force microscope MIDAS (Micro-Imaging Dust Analysis System) [2], and the impact detector GIADA (Grain Impact Analyser and Dust Accumulator) [3]. These three instruments provide complementary insights into dust particles properties over a wide range of sizes/masses (10nm to 1mm). GIADA and MIDAS observed a major contribution from compact dust particles together with a population of porous particles with a low fractal dimension (Df~1,7 for MIDAS [4]) [5, 6]. The fractal dust component of the nucleus and its properties give constraints on the formation of comets in the early solar system [5]. In this work, we analyseresults from a simple numerical model of dust aggregates compactionto assess the initial physical properties of the dust populations.

The Rosetta space mission includes three main instruments for solid dust particles analysis. The combined microscope and mass spectrometer COSIMA (Cometary Secondary Ion Mass Analyser) [1], the atomic force microscope MIDAS (Micro-Imaging Dust Analysis System) [2], and the impact detector GIADA (Grain Impact Analyser and Dust Accumulator) [3]. These three instruments provide complementary insights into the dust particles properties thanks to their different approaches and resolution ranges (10nm to 1mm). GIADA and MIDAS observed a major contribution from compact dust aggregates together with a population of porous particles with a low fractal dimension (Df ~ 1.7 for MIDAS [4]) [5, 6]. Such a fractal dust component of the nucleus and its properties give constraints on the formation of comets in the early solar system [5]. In this work, we analyse results from a simple numerical model of dust aggregates compaction and compare them with COSIMA images of collected aggregates to assess the initial physical properties of the dust populations. We consider 4 different kinds of fractal aggregates presenting different initial fractal dimensions (Df ~ 1.8/2.1/2.5/3) based on their aggregation processes (diffusion limited or reaction limited aggregations, depending on the surface sticking probabilities of the monomers, and particle-cluster or cluster-cluster aggregations). We find that the aspect ratio distribution observed by COSIMA may be explained either by compacting two different initial families with low and high fractal dimensions and the same cohesive strength between monomers, or by compacting a single type of particles (with an aggregation process like DLPA) however with a large range of internal cohesive strengths or collection velocities. References: [1] Kissel, J. et al. (2007) SSR, 128(1), 823-867. [2] Riedler, W. et al. (2007) SSR, 128(1-4), 869-904. [3] Colangeli, L. et al. (2007) SSR, 128(1-4), 803-821. [4] Mannel, T. et al. (2016) MNRAS, 462(S1), 304-311. [5] Fulle, M. and Blum, J. (2017), MNRAS, 469(S2), 39-44 [6] Fulle, M. et al. (2017) MNRAS 469(S2), 45–49