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At least 487 records · Page 27

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗

Exploratory Project: Rigid nanostructured organic polymer monolith for in situ collection and analysis of plant metabolites from soil matrices

Plant metabolites released from litter leachates and root exudates enable plants to adapt and survive in a wide range of habitats by facilitating resource foraging and plant-organismal interactions, and could influence soil carbon storage. The biological functions of these plant inputs and the organismal interactions they facilitate in soil are strictly governed by their composition and molecular identity. Our current understanding about the molecular identity of exudates is based on physiological studies that are done in soil-less axenic cultures. On the other hand, ecological studies that rely on isotope labeling to track the fluxes of carbon from plants to soil have found the complexities of soil-microbe matrices as an insurmountable barrier to undertake any meaningful molecular level characterization of plant inputs. Although it is constantly advocated to undertake a molecular level identification of the dynamicity of plant metabolites in soils, the complexity of soil system has thus far prevented any such endeavors. We developed polymeric probes through in-situ polymerization of poly(styrene-co-vinylbenzyl chloride-co-divinylbenzene) to elucidate the chemical environment of the soil to which the plant roots are exposed. Hypercrosslinking of the polymeric probes through an in-situ Friedel-Crafts alkylation significantly increased the surface area and the sorption capacity of the probes. Surface functionalization of the probes using a hybrid approach was also attempted. The efficacy of these probes was tested using batch equilibration. Scanning electron microscopy revealed extensive modification of the surface of the probes through hypercrosslinking. The probes exhibited a lower site specific sorption (slope of Freundlich adsorption isotherm close to unity) and percent recovery of the sorbed compounds from the probes were >70, indicating a predominance of reversible sorption. Further we imparted specificity to this copolymer matrix by using molecular-template imprinting approach for the selective capture of less abundant plant metabolites from a crowded soil/litter leachate. Our results suggests that i) the root exudate pattern of plants is highly dependent on the nutrient status of the plant, with greater specificity of root exudation occurring in growing medium with low available form of nutrients, ii) the chemical composition of root exudation is a function of the distance of sampling from the source-roots, with the composition of root exudation being more enriched in polar metabolites farther from the source-roots, iii) Further we demonstrated that the compounds present in real root exudates diffuse farther from the source roots than those in artificial root exudates that are traditionally used. Thus, our project highlights how the soil matrix is instrumental in modifying the chemical composition of root exudates, and highlights that, apart from the plant physiology, the specificity and function of root exudates is also modified by environmental factors.

54 ENVIRONMENTAL SCIENCES↗

Using complimentary microscopy methods to examine Ni-Mn-Si-precipitates in highly-irradiated reactor pressure vessel steels

Nano-scale Ni-Mn-Si-rich precipitates formed in a reactor pressure vessel steel under high neutron fluence have been characterized using highly complimentary atom probe tomography (APT) and scanning transmission electron microscopy with energy dispersive spectroscopy (STEM-EDS) combined with STEM-EDS modeling. Using these techniques in a synergistic manner to overcome the well-known trajectory aberrations in APT data, the average upper limit Fe concentration within the precipitates was found to be ~6 at.%. Using this knowledge, accurate compositions of the precipitates was determined and it was found that the spread of precipitate compositions was large, but mostly centered around the Γ2-and G-phases. The use of STEM-EDS also allowed for larger areas to be examined, and segregation of minor solutes was observed to occur on grain boundaries, along with Ni-Mn-Si-rich precipitates that were smaller in size than those in the matrix. Solute segregation at the grain boundaries is proposed to occur through a radiation induced segregation or radiation enhanced diffusion mechanism due to the presence of a denuded zone about the grain boundary. It is also proposed that the reduced precipitate size at the grain boundaries is due to the structure of the grain boundary. The lack of Ni-Mn-Si precipitates observed in larger Mo-rich precipitates is also discussed, and the absence of the minor solutes required to form the Ni-Mn-Si precipitates results in the lack of nucleation. This is in contrast to cementite phases in which Ni-Mn-Si precipitates have been seen to be formed. It was also determined through this work that the exclusion of all the Fe ions during atom probe analysis is a reasonable approximation.

36 MATERIALS SCIENCE↗

Strong Enhancement of Nanoconfined Water Mobility by a Structure Breaking Salt

For the majority of the water present on earth, the two most important factors influencing its behavior are confinement, in either inorganic or organic matrixes, and the presence of solutes. Here, we investigate the effect of confinement in 3 nm pores on water diffusivity in aqueous solutions with archetypical solutes, a structure making (kosmotrope) NaCl and a structure breaking (chaotrope) KCl, up to 1.0 M in concentration. The water diffusivity in bulk aqueous solutions in such a concentration range is known to decrease very slightly in the presence of NaCl and increase very slightly in the presence of KCl. However, here we observe the water diffusivity in confined H 2 O–KCl increases by a factor of 2 compared to the pure water diffusivity in the same confinement. This unusually strong cumulative effect of confinement and a structure breaking additive may have profound implications for the mobility and transport of aqueous species in nature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polyethylene Blends for Improved Oxygen Barrier: Processing-Dependent Microstructure and Gas Permeability

Here this work demonstrates a greater than expected enhancement of oxygen barrier properties in linear low-density polyethylene (LLDPE)-based materials by blending LLDPE with high-density polyethylene (HDPE). The films made by melt pressing the LLDPE/HDPE blends had a greater reduction in oxygen permeability coefficients (PO 2 ) than predicted using common permeability reduction models, i.e., the harmonic average model and zero-permeability nanofiller model. The reduction of PO 2 was attributed to the presence of spherulite crystal structures, as revealed by atomic force microscopy combined with infrared spectroscopy (AFM-IR). The LLDPE matrix exhibited significant spherulite formation even at a relatively low addition of HDPEs, which likely formed tortuous pathways for diffusing oxygen molecules. Transport results from melt-pressed films contrast with the results from films with similar compositions prepared by film blowing, which did not show barrier enhancement beyond expectation. AFM-IR revealed that the blown films lacked spherulite crystals likely due to stretching in the machine direction followed by rapid cooling. These findings demonstrate the role of processing in controlling microstructures and thus the oxygen barrier performance. This work offers the possibility of achieving easily recyclable LLDPE-based packaging materials by simple blending of polyethylenes with different crystalline content.

36 MATERIALS SCIENCE↗

MRI reconstruction of multi-image acquisitions using a rank regularizer with data reordering

Purpose: To improve rank constrained reconstructions for undersampled multi-image MRI acquisitions. Methods: Motivated by the recent developments in low-rank matrix completion theory and its applicability to rapid dynamic MRI, a new reordering-based rank constrained reconstruction of undersampled multi-image data that uses prior image information is proposed. Instead of directly minimizing the nuclear norm of a matrix of estimated images, the nuclear norm of reordered matrix values is minimized. The reordering is based on the prior image estimates. The method is tested on brain diffusion imaging data and dynamic contrast enhanced myocardial perfusion data. Results: Good quality images from data undersampled by a factor of three for diffusion imaging and by a factor of 3.5 for dynamic cardiac perfusion imaging with respiratory motion were obtained. Reordering gave visually improved image quality over standard nuclear norm minimization reconstructions. Root mean squared errors with respect to ground truth images were improved by ∼18% and ∼16% with reordering for diffusion and perfusion applications, respectively. Conclusions: The reordered low-rank constraint is a way to inject prior image information that offers improvements over a standard low-rank constraint for undersampled multi-image MRI reconstructions.

60 APPLIED LIFE SCIENCES↗

Joining and fabrication of metal-matrix composite materials

Manufacturing technology associated with developing fabrication processes to incorporate metal-matrix composites into flight hardware is studied. The joining of composite to itself and to titanium by innovative brazing, diffusion bonding, and adhesive bonding is examined. The effects of the fabrication processes on the material properties and their influence on the design of YF-12 wing panels are discussed.

Royster, D. M.↗

Imaging X-ray spectrometer

An X-ray spectrometer for providing imaging and energy resolution of an X-ray source is described. This spectrometer is comprised of a thick silicon wafer having an embedded matrix or grid of aluminum completely through the wafer fabricated, for example, by thermal migration. The aluminum matrix defines the walls of a rectangular array of silicon X-ray detector cells or pixels. A thermally diffused aluminum electrode is also formed centrally through each of the silicon cells with biasing means being connected to the aluminum cell walls and causes lateral charge carrier depletion between the cell walls so that incident X-ray energy causes a photoelectric reaction within the silicon producing collectible charge carriers in the form of electrons which are collected and used for imaging.

Grant, P. A.↗

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗

CO 2 in Ionene–Ionic Liquid Composite Membranes

Abstract Ionene – ionic liquid (IL) composites are promising materials for CO 2 separation, yet a molecular‐level understanding of their structure and its impact on CO 2 speciation, solubility, rotation, and diffusivity remains unclear. Herein, using multimodal nuclear magnetic resonance (NMR), time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS), atomic force microscopy (AFM), and molecular dynamics (MD) simulations, we reveal that the composites contain IL‐rich domains extending across hundreds of nanometres within the ionene matrix, and these bicontinuous domains span the entire membrane depth. CO 2 also absorbs into the ionene matrix, with the distribution between two CO 2 species varying with temperature and time. The rotational correlation times of these two species are on the timescale of 0.1 and 1 ns, respectively. As IL content increases, the ionic domains expand, resulting in higher CO 2 solubility due to enhanced molecular dynamics and increased free volume in both ionene backbones and IL‐rich regions. Although CO 2 diffusion in the membranes is an order of magnitude slower than in bulk IL, the activation energy for CO 2 diffusion remains comparable. Ionene‐IL composites represent a promising platform for designing CO 2 separation membranes, offering enhanced CO 2 diffusion and selectivity through IL‐rich domains, and increased CO 2 solubility and mechanical integrity from the ionene matrix.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Diffusion Driven Combustion Waves in Porous Media

Filtration of gas containing oxidizer, to the reaction zone in a porous medium, due, e.g., to a buoyancy force or to an external pressure gradient, leads to the propagation of Filtration combustion (FC) waves. The exothermic reaction occurs between the fuel component of the solid matrix and the oxidizer. In this paper, we analyze the ability of a reaction wave to propagate in a porous medium without the aid of filtration. We find that one possible mechanism of propagation is that the wave is driven by diffusion of oxidizer from the environment. The solution of the combustion problem describing diffusion driven waves is similar to the solution of the Stefan problem describing the propagation of phase transition waves, in that the temperature on the interface between the burned and unburned regions is constant, the combustion wave is described by a similarity solution which is a function of the similarity variable x/square root of(t) and the wave velocity decays as 1/square root of(t). The difference between the two problems is that in the combustion problem the temperature is not prescribed, but rather, is determined as part of the solution. We will show that the length of samples in which such self-sustained combustion waves can occur, must exceed a critical value which strongly depends on the combustion temperature T(sub b). Smaller values of T(sub b) require longer sample lengths for diffusion driven combustion waves to exist. Because of their relatively small velocity, diffusion driven waves are considered to be relevant for the case of low heat losses, which occur for large diameter samples or in microgravity conditions, Another possible mechanism of porous medium combustion describes waves which propagate by consuming the oxidizer initially stored in the pores of the sample. This occurs for abnormally high pressure and gas density. In this case, uniformly propagating planar waves, which are kinetically controlled, can propagate, Diffusion of oxidizer decreases the wave velocity. In addition to the reaction and diffusion layers, the uniformly propagating wave structure includes a layer with a pressure gradient, where the gas motion is induced by the production or consumption of the gas in the reaction as well as by thermal expansion of the gas. The width of this zone determines the scale of the combustion wave in the porous medium.

Aldushin, A. P.↗

Using θ' interfaces as templates for planar L1 2 precipitation in AlCuMnZr alloys

Controlled Mn and Zr additions to Al-Cu alloys have allowed for the improved retention of mechanical properties after extended 350°C exposures by stabilizing the main strengthening θ' (Al 2 Cu) phase. Ultimately, θ'/L1 2 (Al 3 Zr) co-precipitate formation stabilizes θ' most effectively; however, Zr diffuses sluggishly and has low solubility in aluminum castings. Increasing the Zr segregation rate would allow for faster and more effective θ'/L1 2 co-precipitation. It is demonstrated that the Zr segregation rate is faster when the Zr matrix content is higher. A much higher Zr matrix content was achieved by rapid cooling during additive manufacturing (AM) that produces θ'/L1 2 co-precipitation faster, which is shown by scanning transmission electron microscopy and atom probe tomography experiments. It was also found that Zr continuously segregates to θ' interfaces up to the most aggressive heat treatment studied such that planar L1 2 precipitates remain after the metastable θ' dissolves. In this manner, we demonstrate that θ' coherent interfaces serve as perfect templates to form stable planar L1 2 precipitates that can provide strength at higher temperatures than traditional θ' strengthened AlCu alloys. This work introduces an alloy design strategy that uses metastable precipitates to quickly nucleate and grow co-precipitates with a desired geometry that contain slow diffusing elements. These ideas can be applied to engineer more heat resistant alloys by taking advantage of high solute matrix contents enabled by rapid cooling during additive manufacturing.

36 MATERIALS SCIENCE↗

Pore-scale modelling of Ostwald ripening

In a saturated solution with dispersed clusters of a second phase, the mechanism by which the larger clusters grow at the expense of the smaller ones is called Ostwald ripening. Although the mechanism is well understood in situations where multiple clusters of gas exist in a liquid solution, evolution is much more complicated to predict when the two phases interact with a solid matrix, since the solid plays a significant role in determining the shape of the interface. In this paper, we study capillary dominated regimes in porous media where the driving force is inter-cluster diffusion. By decomposing the Ostwald ripening mechanism into two processes that operate on different time scales – the diffusion of solute gas in the liquid and the readjustment of the shape of the gas–liquid interface to accommodate a change in mass – we develop a sequential algorithm to solve for the evolution of systems with multiple gas ganglia. In the absence of a solid matrix, thermodynamic equilibrium is reached when all of the gas phase aggregates to form one large bubble. In porous media on the other hand, we find that ripening can lead to equilibrium situations with multiple disconnected ganglia, and that evolution is highly dependent on initial conditions and the structure of the solid matrix. The fundamental difference between the two cases is in the relationship between mass and capillary pressure.

bio-inspired, mechanical behavior, carbon sequestr↗

The tensile failure modes of metal-matrix composite materials

The strengths of individual boron fibers extracted from various as-received and thermally fatigued aluminum alloy matrix materials were measured. The results are described in terms of a Weibull distribution, and strengths of composites fabricated from these fibers are calculated in terms of lower and upper bounds. Tests conducted on composite specimens indicated that strengths approaching the upper bounds can be achieved in composites fabricated by normal diffusion bonding techniques. Cyclic temperature changes effectively reduced the strength values toward the lower bounds. It was concluded that this effect resulted from the degradation of the strength of the fiber-matrix bond.

Wright, M. A.↗

Grain Growth in Nanocrystalline Mg-Al Thin Films

An improved understanding of grain growth kinetics in nanocrystalline materials, and in metals and alloys in general, is of continuing interest to the scientific community. In this study, Mg - Al thin films containing ~10 wt.% Al and with 14.5 nm average grain size were produced by magnetron-sputtering and subjected to heat-treatments. The grain growth evolution in the early stages of heat treatment at 423 K (150 °C), 473 K (200 °C) and 573K (300 °C) was observed with transmission electron microscopy and analyzed based upon the classical equation developed by Burke and Turnbull. The grain growth exponent was found to be 7±2 and the activation energy for grain growth was 31.1±13.4 kJ/mol, the latter being significantly lower than in bulk Mg-Al alloys. The observed grain growth kinetics are explained by the Al supersaturation in the matrix and the pinning effects of the rapidly forming beta precipitates and possibly shallow grain boundary grooves. The low activation energy is attributed to the rapid surface diffusion which is dominant in thin film systems.

activation energy↗

Optimization of four terminal rear heterojunction GaAs on Si interdigitated back contact tandem solar cells

High-efficiency, four-terminal tandem solar cells composed of thin GaAs films mechanically stacked onto interdigitated back contact silicon solar cells with a glass interlayer are demonstrated. The optimal thickness of the absorber layer of a rear heterojunction GaAs subcell for use in four terminal tandem solar cells was studied. GaAs top cells with absorber layer thicknesses of 1.5, 1.9, 2.3, 2.8, and 3.5 µm were fabricated on glass and mechanically stacked onto interdigitated back-contact Si bottom cells. All tandem cells were found to have efficiencies above 30% under the AM1.5 G spectrum demonstrating a relatively weak sensitivity to thickness in the four-terminal configuration. We found the 2.8 µm absorber layer cell to have the highest top cell and tandem cell efficiency at 26.38% and 32.57%, respectively. Optical modeling with transfer matrix method for the planar top cell and Lambertian light trapping in the textured Si subcell, along with drift-diffusion Hovel equations, were used to show photon recycling enhancement to the effective diffusion length and VOC of the top cell as a result of the low-index glass interlayer.

14 SOLAR ENERGY↗

On the delta-type doping of GaAs-based heterostructures with manganese compounds

Heterostructures, which incorporate GaAs/InGaAs/GaAs quantum wells and are doped with spatially remote monatomic Mn layers, are formed on GaAs(001) substrate under conditions of multilayer buildup by the method of molecular-beam epitaxy. Combined studies of the obtained samples were performed by the method of secondary-ion mass spectrometry, by measurements of X-ray diffraction, and using a transmission electron microscope. The heterostructures under study with a doping impurity concentration amounting to 0.5 single layers are elastically stressed and demonstrate planar clearly defined interfaces without visible extended or point defects. A method for visualization of the distribution of the manganese concentration in the three-dimensional GaAs matrix in the vicinity of a quantum well is suggested. According to experimental results, there is a probability for manganese diffusion into the GaAs/InGaAs/GaAs quantum well when the critical thickness of the GaAs buffer layer is decreased to a value smaller than 3 nm.

36 MATERIALS SCIENCE↗

Multifrequency imaging radar polarimetry: Depolarisation of radar echoes at three wavelengths

It is shown that high resolution imaging radar polarimeters can describe depolarization effects in great detail by measuring the complete Stokes matrix for small regions on the Earth's surface, permitting to distinguish between coherent polarization transformation by the surface and diffuse interactions that randomize the polarization state of the received wave. Multiwavelength polarimeter observations of a variety of types of terrain, including images of the coherent and diffuse parts of the received signal are presented. The diffuse image, in particular, is highly indicative of small-scale surface roughness, an effect illustrated by analyzing a set of polarimeter images acquired over lava fields of varying roughness.

Zebker, H. A.↗