Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135885/1/srtan_1.pd

Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137141/1/srtan_1.pd

Wideband Instrument for Snow Measurements (WISM)

This presentation discusses current efforts to develop a Wideband Instrument for Snow Measurements (WISM). The objective of the effort are as follows: to advance the utility of a wideband active and passive instrument (8-40 gigahertz) to support the snow science community; improve snow measurements through advanced calibration and expanded frequency of active and passive sensors; demonstrate science utility through airborne retrievals of snow water equivalent (SWE); and advance the technology readiness of broadband current sheet array (CSA) antenna technology for spaceflight applications

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number z_{c} of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of z_{c} and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ν_{c}=z_{c}ϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.ISSN:1539-3755ISSN:1063-651XISSN:1095-3787ISSN:1550-237

Band calculations using broadband Green’s functions and the KKR method with applications to magneto-optics and photonic crystals

In this paper, we develop a method of simulations of using the broadband Green’s function (BBGF) in the Korringa Kohn Rostoker (KKR) method. The merit of the method is broadband such that once the initial setup is completed, the calculation at every frequency is calculated rapidly. The broadband Green’s function consists of a frequency-independent spatial summation and a spectral summation that has most of the factors frequency independent. Both summations have fast convergence. Analytical expressions of broadband coefficients of cylindrical waves are derived from the BBGF. The broadband cylindrical waves coefficients are then combined with the KKR method to calculate the determinant equation for a wide range of frequencies. Numerical results of the band diagrams and band surface currents are illustrated for magneto-optics and photonic crystals. The CPU time requirements, including setup, using MATLAB on a standard laptop, for computing the determinant at 1000 frequencies at a Bloch vector are 0.411 s and 1.206 s, respectively, for the cases of topological crystal of small scatterer relative to cell size and the photonic crystal of large scatterer comparable to cell size

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

We have conducted discrete element simulations (PFC3D) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number zc of cohesive contacts and particle volume fraction f of the initial states. We focus on discerning the role of zc and f for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density.c = zcf of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure

Snow Water Equivalent Retrieval Using Active and Passive Microwave Observations

This paper implements a newly developed combined active and passive algorithm for the retrieval of snow water equivalent (SWE) by using three- channel active and two- channel passive observations. First, passive microwave observations at 19 and 37 GHz are used to determine the scattering albedo of snow. An a priori scattering albedo is obtained by averaging over time series observations. Second, 13.3 GHz is introduced to formulate a three- channel (9.6, 13.3, and 17.2 GHz) radar algorithm which reduces effects of background scattering from the snow- soil interface, and improves SWE retrieval. In the algorithm, the bicontinuous dense media radiative transfer (DMRT- Bic) is used to compute look- up tables (LUTs) of both radar backscatter and radiometer brightness temperatures (TBs) of the snowpack. To accelerate the retrieval, a parameterized model is derived from LUT by regression training, which links backscatter to the scattering albedo at 9.6 GHz or 13.3 GHz and to SWE. The volume scattering of snow is obtained by subtracting the background scattering from radar observations. SWE is then retrieved through a cost function that is guided by the a priori scattering albedo obtained from the passive microwave observations. The proposed algorithm, along with the active- only version, is evaluated against the Finnish Nordic Snow Radar Experiment (NoSREx) data set measured in 2009- 2013. The combined active- passive algorithm achieves root mean square errors (RSME) less than 27 mm and correlation coefficients above 0.68 for 2009- 2010, RMSE less than 21 mm and correlation above 0.85 for 2010- 2011, and RMSE less than 40 mm and correlation above 0.38 for 2012- 2013.Key PointsSnow water equivalent retrieval using X (9.6 GHz) and upper Ku band (17.2 GHz) radar observations is improved by adding lower Ku- band (13.3 GHz) dataPassive observations are used to obtain scattering albedos, which improves the radar retrieval algorithm performanceThe resulting combined active and passive algorithm is validated against the Finnish NoSREx datasetPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/168354/1/wrcr25382_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/168354/2/wrcr25382.pd

Snow Water Equivalent Retrieval Using Active and Passive Microwave Observations

This paper implements a newly developed combined active and passive algorithm for the retrieval of snow water equivalent (SWE) by using three- channel active and two- channel passive observations. First, passive microwave observations at 19 and 37 GHz are used to determine the scattering albedo of snow. An a priori scattering albedo is obtained by averaging over time series observations. Second, 13.3 GHz is introduced to formulate a three- channel (9.6, 13.3, and 17.2 GHz) radar algorithm which reduces effects of background scattering from the snow- soil interface, and improves SWE retrieval. In the algorithm, the bicontinuous dense media radiative transfer (DMRT- Bic) is used to compute look- up tables (LUTs) of both radar backscatter and radiometer brightness temperatures (TBs) of the snowpack. To accelerate the retrieval, a parameterized model is derived from LUT by regression training, which links backscatter to the scattering albedo at 9.6 GHz or 13.3 GHz and to SWE. The volume scattering of snow is obtained by subtracting the background scattering from radar observations. SWE is then retrieved through a cost function that is guided by the a priori scattering albedo obtained from the passive microwave observations. The proposed algorithm, along with the active- only version, is evaluated against the Finnish Nordic Snow Radar Experiment (NoSREx) data set measured in 2009- 2013. The combined active- passive algorithm achieves root mean square errors (RSME) less than 27 mm and correlation coefficients above 0.68 for 2009- 2010, RMSE less than 21 mm and correlation above 0.85 for 2010- 2011, and RMSE less than 40 mm and correlation above 0.38 for 2012- 2013.Key PointsSnow water equivalent retrieval using X (9.6 GHz) and upper Ku band (17.2 GHz) radar observations is improved by adding lower Ku- band (13.3 GHz) dataPassive observations are used to obtain scattering albedos, which improves the radar retrieval algorithm performanceThe resulting combined active and passive algorithm is validated against the Finnish NoSREx datasetPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/168354/1/wrcr25382_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/168354/2/wrcr25382.pd