Dense Discrete Random Media Research Articles

Scattering, absorption, and thermal emission by large cometary dust particles: Synoptic numerical solution

Context.Remote light scattering and thermal infrared observations provide clues about the physical properties of cometary and interplanetary dust particles. Identifying these properties will lead to a better understanding of the formation and evolution of the Solar System.Aims.We present a numerical solution for the radiative and conductive heat transport in a random particulate medium enclosed by an arbitrarily shaped surface. The method will be applied to study thermal properties of cometary dust particles.Methods.The recently introduced incoherent Monte Carlo radiative transfer method developed for scattering, absorption, and propagation of electromagnetic waves in dense discrete random media is extended for radiative heat transfer and thermal emission. The solution is coupled with the conductive Fourier transport equation that is solved with the finite-element method.Results.The proposed method allows the synoptic analysis of light scattering and thermal emission by large cometary dust particles consisting of submicrometer-sized grains. In particular, we show that these particles can sustain significant temperature gradients resulting in the superheating factor phase function observed for the coma of comet 67P/Churyumov–Gerasimenko.

Dependent scattering and absorption by densely packed discrete spherical particles: Effects of complex refractive index

Due to the dependent scattering and absorption effects, the radiative transfer equation (RTE) may not be suitable for dealing with radiative transfer in dense discrete random media. This paper continues previous research on multiple and dependent scattering in densely packed discrete particle systems, and puts emphasis on the effects of particle complex refractive index. The Mueller matrix elements of the scattering system with different complex refractive indexes are obtained by both electromagnetic method and radiative transfer method. The Maxwell equations are directly solved based on the superposition T-matrix method, while the RTE is solved by the Monte Carlo method combined with the hard sphere model in the Percus-Yevick approximation (HSPYA) to consider the dependent scattering effects. The results show that for densely packed discrete random media composed of medium size parameter particles (equals 6.964 in this study), the demarcation line between independent and dependent scattering has remarkable connections with the particle complex refractive index. With the particle volume fraction increase to a certain value, densely packed discrete particles with higher refractive index contrasts between the particles and host medium and higher particle absorption indexes are more likely to show stronger dependent characteristics. Due to the failure of the extended Rayleigh-Debye scattering condition, the HSPYA has weak effect on the dependent scattering correction at large phase shift parameters.

Multiple and dependent scattering by densely packed discrete spheres: Comparison of radiative transfer and Maxwell theory

The radiative transfer equation (RTE) has been widely used to deal with multiple scattering of light by sparsely and randomly distributed discrete particles. However, for densely packed particles, the RTE becomes questionable due to strong dependent scattering effects. This paper examines the accuracy of RTE by comparing with the exact electromagnetic theory. For an imaginary spherical volume filled with randomly distributed, densely packed spheres, the RTE is solved by the Monte Carlo method combined with the Percus–Yevick hard model to consider the dependent scattering effect, while the electromagnetic calculation is based on the multi-sphere superposition T-matrix method. The Mueller matrix elements of the system with different size parameters and volume fractions of spheres are obtained using both methods. The results verify that the RTE fails to deal with the systems with a high-volume fraction due to the dependent scattering effects. Apart from the effects of forward interference scattering and coherent backscattering, the Percus–Yevick hard sphere model shows good accuracy in accounting for the far-field interference effects for medium or smaller size parameters (up to 6.964 in this study). For densely packed discrete spheres with large size parameters (equals 13.928 in this study), the improvement of dependent scattering correction tends to deteriorate. The observations indicate that caution must be taken when using RTE in dealing with the radiative transfer in dense discrete random media even though the dependent scattering correction is applied.

Paddy Fields as Electrically Dense Media: Theoretical Modeling and Measurement Comparisons

Early models for paddy fields consist of a single-layered medium in which coherent effects within clusters of leaves are considered but multiple volume scattering is not. In this paper, the paddy canopy is modeled as a multilayered dense discrete random medium consisting of cylindrical and needle-shaped scatterers. Consideration is given to the coherent and near-field effects of the closely spaced scatterers through the Dense Medium Phase and Amplitude Correction Theory and Fresnel corrections, respectively, in the phase matrix. Then, this dense medium phase matrix is applied in the radiative transfer equations and solved up to the second order to consider double-volume scattering. Ground truth measurements of paddy fields were acquired at Sungai Burung, Selangor, Malaysia, for an entire season from the early vegetative stage of the plants to their reproductive stage. Measured parameters are used in the theoretical model to calculate the backscattering coefficients of paddy fields. Theoretical analysis of the simulation results shows in particular that second-order effects are important for cross-polarized backscatter data and that coherent effects need to be considered at lower frequencies. However, the use of needles to represent paddy leaves tends to underestimate the HH-polarized backscattering coefficients especially at the latter stages of plant growth, i.e., when the leaves are broader. The results are also used for comparisons with the backscattering coefficients obtained from RADARSAT images as well as that of earlier models to test the validity of the dense medium model with promising results.

Theoretical Modeling and Measurement Comparison of Season-Long Rice Field Monitoring

The development of a theoretical model to describe the scattering mechanisms involved in the remote sensing of rice crops is essential, as it ensures correct application of remote sensing data for rice monitoring. The theoretical model used in this study is based on the radiative transfer theory applied on a layered dense discrete random medium. The dense medium phase and amplitude correction theory (DM-PACT), which considers the coherent effects of the scatterers, is incorporated in the development of the phase matrices of the scatterers, which are modeled after the physical geometry of the plants. Ground truth measurements of rice fields were acquired at Sungai Burung, Selangor, Malaysia for an entire season. These measurements are used in the theoretical model to calculate the backscattering coefficients of rice fields. The results are then compared to those obtained from RADARSAT images to test the validity of the model. Comparisons show promising results, but further research is required to improve on the current model.

Scattering of electromagnetic waves from dense distributions of spheroidal particles based on Monte Carlo simulations.

In a dense discrete random medium, the propagation and scattering of waves are affected not only by the individual properties of the particles such as size, shape, and permittivity, but also by group properties such as the statistics of relative particle positions and relative orientations. We use Monte Carlo simulations to investigate the interactions of electromagnetic waves with a dense medium consisting of spheroidal particles for cases of random orientation and for cases of aligned orientation. A shuffling process is used to generate the positions of densely packed spheroids. Multiple-scattering equations are formulated by means of the volume integral equation and are solved numerically. The scattering results are averaged over realizations. Numerical results are presented for the extinction rates and the phase matrices. Salient features of the numerical results indicate that (1) the extinction rates of densely packed small spheroids are smaller than those of independent scattering; (2) for aligned spheroids, the extinction rates are polarization dependent; and (3) the co-polarized part of the phase matrix for densely packed spheroids is smaller than that of independent scatering, while the cross-polarized part is larger than that for independent scattering. This means that the ratio of cross-polarization to co-polarization is significantly higher than that of independent scattering.

Radar backscatter from a dense discrete random medium

A dense medium phase matrix developed based on the concept of random lattice perturbation is employed in the radiative transfer theory to calculate the coand cross-polarized backscatter from a layer of randomly distributed spherical scatterers. The position randomness properties are characterized by the variance and correlation function of scatterer positions within the medium. The dense medium phase matrix differs from the conventional one in two major aspects, i.e., there is an amplitude and a phase correction. These corrections account for the effects of close spacing and position correlation between scatterers in a dense discrete random medium. This study shows that phase coherency and close-spacing amplitude modifications are two separate corrections necessary for an electrically dense medium. Results indicate that there is a need to distinguish between spatially and electrically dense medium. The phase correction is found to have a greater impact on cross-polarized than like-polarized backscatter coefficients; the converse is true of the amplitude correction. Backscattering calculations from the theory are compared with measurements from controlled microwave experiments on random media consisting of closely packed spheres, and from field measurements of dry snowpack. Predictions from such a theory agree well with the measured data.

A phase matrix for a dense discrete random medium: evaluation of volume scattering coefficient

In the derivation of the conventional scattering phase matrix of a discrete random medium, the far-field approximation is usually assumed. In this paper, the phase matrix of a dense discrete random medium is developed by relaxing the far-field approximation and accounting for the effect of volume fraction and randomness properties characterized by the variance and correlation function of scatterer positions within the medium. The final expression for the phase matrix differs from the conventional one in two major aspects: there is an amplitude and a phase correction. The concept used in the derivation is analogous to the antenna array theory. The phase matrix for a collection of scatterers is found to be the Stokes matrix of the single scatterer multiplied by a dense medium phase correction factor. The close spacing amplitude correction appears inside the Stokes matrix. When the scatterers are uncorrelated, the phase correction factor approaches unity. The phase matrix is used to calculate the volume scattering coefficients for a unit volume of spherical scatterers, and the results are compared with calculations from other theories, numerical simulations, and laboratory measurements. Results indicate that there should be a distinction between physically dense medium and electrically dense medium.

Monte Carlo Simulations of Pair Distribution Functions of Dense Discrete Random Media With Multiple Sizes of Particles

In a dense discrete random medium, the propagation and scattering of waves are affected by the statistics of the particle positions. For the case of particles of finite size, the positions of the particles relative to each other in the presence of other particles are correlated and the second order statistics are described by the pair distribution functions. In this paper, we perform Monte Carlo simulations of pair distribution functions of dense discrete random media consisting of particles of multiple sizes. The Metropolis technique and the sequential random addition of particles methods are used to generate a series of configurations through random processes. The pair distribution functions are calculated by counting the average occurrence of pair separation of particles. The Monte Carlo results of the particle pair distribution functions are illustrated and are compared with the results of the Percus-Yevick approximation. The results from the two Monte Carlo methods are found to be in good agreement.