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DOE OSTI2024

Overcoming obstacles to IPv6 on WLCG

The transition of the Worldwide Large Hadron Collider Computing Grid (WLCG) storage services to dual-stack IPv6/IPv4 is almost complete; all Tier-1 and 94% of Tier-2 storage are IPv6 enabled. While most data transfers now use IPv6, a significant number of IPv4 transfers still occur even when both endpoints support IPv6. This paper presents the ongoing efforts of the HEPiX IPv6 working group to steer WLCG toward IPv6-only services by investigating and fixing the obstacles to the use of IPv6 and identifying cases where IPv4 is used when IPv6 is available. Removing IPv4 use is essential for the long-term agreed goal of IPv6-only access to resources within WLCG, thus eliminating the complexity and security concerns associated with dual-stack services. We present our achievements and ongoing challenges as we navigate the final stages of the transition from IPv4 to IPv6 within WLCG.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

An Economic Model of a Steam Accumulator Storage System for Nuclear Power Plants

The growth of non-dispatchable renewables benefits technologies with flexible load capabilities. Baseload technologies must accept low prices and revenues during low-demand periods that arise with increasing frequency as renewables deployment grows. For this reason, generators such as combined cycle gas turbines threaten to out-compete baseload, and nuclear power plants are facing early retirement. If utilities are to consider future nuclear power plants to be attractive investments they must excel at roles other than baseload generation. Energy storage offers a means to avoid times of low prices and capitalize on times of high prices, as well as for nuclear to participate in ancillary markets and provide grid stability and regulation services. This work explores the design of a steam accumulator system that can store energy from a nuclear plant. An economic model is created to determine the market conditions that will produce a profitable system. An energy storage capacity of 500 MWh is chosen as a base case, but the energy to power ratio (E/P ratio) is varied in sensitivity analyses while holding energy fixed. This paper first presents the proposed size and layout of the steam accumulator system. Next, it provides an overview of the thermodynamic model, which is used to determine the system size for base case conditions. An economic model is presented with sensitivity analyses, which show the effect of price volatility on net revenue. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Long-Duration High-Resolution Large-Eddy Simulations of Hurricane Laura (2020) for Infrastructure Design

This dataset provides long-duration large-eddy simulations (LES) of Hurricane Laura (2020), capturing the turbulent boundary-layer wind field during the storm's passage at horizontal grid spacings of 55.55 m and 10 m. Hurricane Laura made landfall as a Category 4 storm in southwestern Louisiana at 06:00 UTC on 27 August 2020, producing widespread damage to coastal infrastructure. The simulations characterize the spatial and temporal variability of the turbulent wind at heights spanning the lowest 300 m of the boundary layer, throughout the approach and passage of the storm's eyewall over a fixed location. To resolve the spatial heterogeneity of wind and turbulence conditions across the storm, seven independent refined LES runs are performed at radial locations spanning the storm relative to its direction of motion. The refinement positions are defined on a normalized radial coordinate r ̂=r/R, where R≈21 km is Laura's radius of maximum wind, and lie between r ̂=-1.5 and r ̂=+1.5 in ∆r ̂=0.5 increments along a line perpendicular to the storm's track at the midpoint of the simulation. Negative r ̂ corresponds to locations south-southwest of the storm center and positive r ̂ to locations north-northeast. The dataset is segmented into seven radial refinement groups.

17 WIND ENERGY↗

NASA NTRS1992

Computational investigation of slot blowing for fuselage forebody flow control

This paper presents a computational investigation of a tangential slot blowing concept for generating lateral control forces on an aircraft fuselage forebody. The effects of varying both the jet width and jet exit velocity for a fixed location slot are analyzed. This work is aimed at aiding researchers in designing future experimental and computational models of tangential slot blowing. The primary influence on the resulting side force of the forebody is seen to be the jet mass flow rate. This influence is sensitive to different combinations of slot widths and jet velocities over the range of variables considered. Both an actuator plane and an overset grid technique are used to model the tangential slot. The overset method successfully resolves the details of the actual slot geometry, extending the generality of the numerical method. The actuator plane concept predicts side forces similar to those produced by resolving the actual slot geometry.

Murman, Scott M.↗

DOE OSTI2013

Dynamic Analysis of Hybrid Energy Systems under Flexible Operation and Variable Renewable Generation -- Part I: Dynamic Performance Analysis and Part II: Dynamic Cost

Dynamic analysis of hybrid energy systems (HES) under flexible operation and variable renewable generation is considered in order to better understand various challenges and opportunities associated with the high system variability arising from the integration of renewable energy into the power grid. Unique consequences are addressed by devising advanced HES solutions in which multiple forms of energy commodities, such as electricity and chemical products, may be exchanged. Dynamic models of various unit operations are developed and integrated within two different HES options. One HES option, termed traditional, produces electricity only and consists of a primary heat generator (PHG) (e.g., a small modular reactor), a steam turbine generator, a wind farm, and a battery storage. The other HES option, termed advanced, includes not only the components present in the traditional option but also a chemical plant complex to repurpose excess energy for non-electricity services, such as for the production of chemical goods (e.g., transportation fuel). In either case, a given HES is connected to the power grid at a point of common coupling and requested to deliver a certain electricity generation profile as dictated by a regional power grid operator based on a predicted demand curve. Dynamic analysis of these highly-coupled HES are performed to identify their key dynamical properties and limitations and to prescribe solutions for best managing and mitigating the high variability introduced from incorporating renewable energy into the energy mix. A comparative dynamic cost analysis is also conducted to determine best HES options. The cost function includes a set of metrics for computing fixed costs, such as fixed operations and maintenance (O&M) and overnight capital costs, and also variable operational costs, such as cost of variability, variable O&M cost, and cost of environmental impact, together with revenues. Assuming different options for implementing PHG (e.g., natural gas, coal, nuclear), preliminary results identify the level of renewable penetration at which a given advanced HES option (e.g., a nuclear hybrid) becomes increasingly more economical than a traditional electricity-only generation solution. Conditions are also revealed under which carbon resources may be better utilized as carbon sources for chemical production rather than as combustion material for electricity generation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Temporal Coarse Graining for Classical Stochastic Noise in Quantum Systems

Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for 1/f noise in solid-state quantum information processors. Here we present an approach for simulating Hamiltonian classical stochastic noise that performs temporal coarse-graining by effectively integrating out the high-frequency components of the noise. We focus on the case where the stochastic noise can be expressed as a sum of Ornstein-Uhlenbeck processes. Temporal coarse-graining is then achieved by conditioning the stochastic process on a coarse realization of the noise, expressing the conditioned stochastic process in terms of a sum of smooth, deterministic functions and bridge processes with boundaries fixed at zero, and performing the ensemble average over the bridge processes. For Ornstein-Uhlenbeck processes, the deterministic components capture all dependence on the coarse realization, and the stochastic bridge processes are not only independent but taken from the same distribution with correlators that can be expressed analytically, allowing the associated noise propagators to be precomputed once for all simulations. This combination of noise trajectories on a coarse time grid and ensemble averaging over bridge processes has practical advantages, such as a simple concatenation rule, that we highlight with numerical examples.

Albash, Tameem [Sandia National Lab. (SNL-NM), Alb↗

DOE OSTI2024

Innovating the next generation of commercial smart building software

Nearly 30% of commercial building energy use is wasted due to equipment faults and HVAC controls problems. The result is increased emissions, compromised comfort and productivity, and less reliable coordination of building power needs with a clean grid. The energy impact alone represents $17 billion in potential savings. Today’s smart building software provides a robust solution to address these operational deficiencies. Energy management and information systems (EMIS) are saving up to 9% on average, with two-year paybacks. They are being incorporated into energy management processes, commissioning services, and utility programs. As effective as they are, two barriers prevent even deeper benefits; limited personnel to fix problems once they are identified, and the expense and time to manually implement changes in control systems. In partnership with the research community, the EMIS industry is developing new capabilities to overcome these barriers. Moving beyond siloed products for either fault detection and diagnostics, or optimal control, these new capabilities empower users to not only automatically identify faults, but also to push corrective action, and control improvements to their buildings. In this paper, several areas for enhancements are documented: ‘one-time’ correction of faults such as setpoints, schedules, and economizer lockouts; short-term active testing for automated proportional integral derivative (PID) loop tuning and functional testing; and continuous supervisory control for demand flexibility and year-round efficiency. Results are presented from a pair of partner implementations out of a dozen providers integrating these enhancements into their products, including field tests from across the country, and insights into operator acceptance and integration into operations and maintenance practices.

Casillas, Armando↗

DOE OSTI2012

VERIFICATION OF THE SHIFT MONTE CARLO CODE

Shift is a new hybrid Monte Carlo/deterministic radiation transport code being developed at Oak Ridge National Laboratory. At its current stage of development, Shift includes a fully-functional parallel Monte Carlo capability for simulating eigenvalue and fixed-source multigroup transport problems. This paper focuses on recent efforts to verify Shift s Monte Carlo component using the two-dimensional and three-dimensional C5G7 NEA benchmark problems. Comparisons were made between the benchmark eigenvalues and those output by the Shift code. In addition, mesh-based scalar flux tally results generated by Shift were compared to those obtained using MCNP5 on an identical model and tally grid. The Shift-generated eigenvalues were within three standard deviations of the benchmark and MCNP5 values in all cases. The flux tallies generated by Shift were found to be in very good agreement with those from MCNP

42 ENGINEERING↗

DOE OSTI2012

Verification of the shift Monte Carlo code with the C5G7 reactor benchmark

Shift is a new hybrid Monte Carlo/deterministic radiation transport code being developed at Oak Ridge National Laboratory. At its current stage of development, Shift includes a parallel Monte Carlo capability for simulating eigenvalue and fixed-source multigroup transport problems. This paper focuses on recent efforts to verify Shift's Monte Carlo component using the two-dimensional and three-dimensional C5G7 NEA benchmark problems. Comparisons were made between the benchmark eigenvalues and those output by the Shift code. In addition, mesh-based scalar flux tally results generated by Shift were compared to those obtained using MCNP5 on an identical model and tally grid. The Shift-generated eigenvalues were within three standard deviations of the benchmark and MCNP5-1.60 values in all cases. The flux tallies generated by Shift were found to be in very good agreement with those from MCNP. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Climate change-resilient snowpack estimation in the Western United States

Abstract In the 21st century, warmer temperatures and changing atmospheric circulation will likely produce unprecedented changes in Western United States snowfall 1–3 , with impacts on the timing, amount, and spatial patterns of snowpack 4–7 . The ~900 snow pillow stations are indispensable to water resource management by measuring snow-water equivalent (SWE) 8,9 in strategic but fixed locations 10,11 . However, this network may not be impacted by climate change in the same way as the surrounding area 12 and thus fail to accurately represent unmeasured locations; climate change thereby threatens our ability to measure the effects of climate change on snow. In this work, we show that maintaining the current peak SWE estimation skill is nonetheless possible. We find that explicitly including spatial correlations—either from gridded observations or learned by the model—improves skill at predicting distributed snowpack from sparse observations by 184%. Existing artificial intelligence methods can be useful tools to harness the many available sources of snowpack information to estimate snowpack in a nonstationary climate.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1987

Communication training for aircrews: A review of theoretical and pragmatic aspects of training program design

This study is the final report of a project studying methods of communications training applicable to both civilian and military aviation personnel, including multiperson teams or single pilot fixed wing or rotary wing aircraft. A review is provided of a number of theories proposed as relevant for producing training materials for improved communications. Criteria are given for evaluating the applicability of training programs to the aviation environment, and these criteria are applied to United Airlines' Resources Management Training, as well as to a number of commercially available general purpose training programs. The report considers in detail assertiveness training and grid management training, examining their theoretical background and attempts made to validate their effectiveness. It was found that there are substantive difficulties in assessing the effectiveness of both training programs, as well as problems with the theories underlying them. However, because the aviation environment offers unique advantages for studying the effectiveness of communications training, recommendations are made on the design of appropriate training programs and on procedures that might be used to validate them.

Linde, Charlotte↗

NASA NTRS2005

Proceedings of the 2004 NASA/ONR Circulation Control Workshop, Part 2

This conference proceeding is comprised of papers that were presented at the NASA/ONR Circulation Control Workshop held 16-17 March 2004 at the Radisson-Hampton in Hampton, VA. Over two full days, 30 papers and 4 posters were presented with 110 scientists and engineers in attendance, representing 3 countries. As technological advances influence the efficiency and effectiveness of aerodynamic and hydrodynamic applications, designs, and operations, this workshop was intended to address the technologies, systems, challenges and successes specific to Coanda driven circulation control in aerodynamics and hydrodynamics. A major goal of this workshop was to determine the state-of-the-art in circulation control and to assess the future directions and applications for circulation control. The 2004 workshop addressed applications, experiments, computations, and theories related to circulation control, emphasizing fundamental physics, systems analysis, and applied research. The workshop consisted of single session oral presentations, posters, and written papers that are documented in this unclassified conference proceeding. The format of this written proceeding follows the agenda of the workshop. Each paper is followed with the presentation given at the workshop. the editors compiled brief summaries for each effort that is at the end of this proceeding. These summaries include the paper, oral presentation, and questions or comments that occurred during the workshop. The 2004 Circulation Control Workshop focused on applications including Naval vehicles (Surface and Underwater vehicles), Fixed Wing Aviation (general aviation, commercial, cargo, and business aircraft); V/STOL platforms (helicopters, military aircraft, tilt rotors); propulsion systems (propellers, jet engines, gas turbines), and ground vehicles (automotive, trucks, and other); wind turbines, and other nontraditional applications (e.g., vacuum cleaner, ceiling fan). As part of the CFD focus area of the 2004 CC Workshop, CFD practitioners were invited to compute a two-dimensional benchmark problem for which geometry, flow conditions, grids, and experimental data were available before the workshop. The purpose was to accumulate a database of simulations for a single problem using a range of CFD codes, turbulence models, and grid strategies so as to expand knowledge of model performance/requirements and guide simulation of practical CC configurations.

Jones, Gregory S.↗

DOE OSTI2017

Does the Perfect Waste Package Exist? Development of a Decisional Tool Addressing this Challenge - 17053

The definition of a safe, technically, economically and societally acceptable waste management strategy is highly dependent on the Waste Acceptance Criteria in each country and on the already available disposal routes. It is the reason why there is not a single solution but a combination of optimized solutions depending on the type of waste and on each country's considerations. In fact, when operating a nuclear plant or performing its decommissioning or legacy waste management, one has to consider a large waste diversity in term of natures, types, volumes and radioactivity spectra. All nuclear operators have to take-up the challenge of implementing solutions for conditioning its waste in packages suitable for transport short to long term interim storage and final disposal of it (or prepare for final disposal if the repository is not yet available). Operators have then to answer the following dilemma: either define a complete strategy packaging the waste for final disposal, or 'containerising' it temporarily, pending final disposal. The strategy is highly country dependent; in the first case, one has to take into account the available information and future orientations relative to acceptability of the packages in order to define a robust solution. The approach implemented in France requires a close dialogue between the Operators, the Safety Authority, the Administration and the stakeholders. Moreover it pushes forward whenever possible standardization, contributing to cost minimization. If the second approach has the advantage of leaving the options open, and reducing the initial investments, it inevitably requires future retrieval and re-packaging with potential evolutions/degradation of the initial waste form. It also induces the potential risk to produce additional secondary waste. As an additional drawback, it introduces uncertainties and unknowns related to the future waste management criteria and to the costs. The general idea is that, depending on context, a given route (i.e., treatment, conditioning, and transport), could be considered as efficient or not. Assessing a waste package is certainly highly context dependent. However it should be possible to recognize and to lead an evaluation based on a number of fixed criteria, whatever the context, to be addressed when assessing the development of a final waste package in connection to the overall management route. A waste package is always a combination of a waste container and a waste form and will have to be transported one day from the production site to the final repository or to off-site interim storage facilities. AREVA's approach consists in defining an evaluation grid based on a set of criteria which aim (i) to evaluate whether the different waste treatments, conditionings, transport and packages deserve to be considered within different national contexts, and (ii) to evaluate R and D actions to be performed for improving existing solutions or developing new ones. One of the key lessons to be drawn from AREVA's experience in developing waste packages is that the perfect waste doesn't exist even though the vitrified canister is probably the most efficient one. The performance of a package resulting from a compromise depends on context and is a strength combination between the waste container and the waste form. The approach is to evaluate a waste package development against different set of criteria and to draw optimization diagrams. In such diagram, a given waste package is assessed with respect to selected criteria such as waste form and waste container, stability, level of waste incorporation, integrity lifetime, secondary waste generation, transport, long term behavior, and economical effectiveness, etc. Addressing a waste form is a very key point. This evaluation grid and comparative approach will be presented through examples and comparison providing from AREVA feedback on waste package development related to complex waste management such as problematic waste or legacy waste. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2017

Scheduling Non-Preemptible Jobs to Minimize Peak Demand

Our paper examines an important problem in smart grid energy scheduling; peaks in power demand are proportionally more expensive to generate and provision for. The issue is exacerbated in local microgrids that do not benefit from the aggregate smoothing experienced by large grids. Demand-side scheduling can reduce these peaks by taking advantage of the fact that there is often flexibility in job start times. We then focus attention on the case where the jobs are non-preemptible, meaning once started, they run to completion. The associated optimization problem is called the peak demand minimization problem, and has been previously shown to be NP-hard. These results include an optimal fixed-parameter tractable algorithm, a polynomial-time approximation algorithm, as well as an effective heuristic that can also be used in an online setting of the problem. Simulation results show that these methods can reduce peak demand by up to 50% versus on-demand scheduling for household power jobs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO 2 , temperature, water, and nitrogen (version 1.0)

Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2020

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO2, temperature, water, and nitrogen (version 1.0)

James A Franke↗

DOE OSTI2016

On the Degradation of the Effectiveness of Nonlinear Diffusion Acceleration with Parallel Block Jacobi Splitting

MOOSE's radiation transport module Rattlesnake comprises a first order S N solver that can be accelerated with a flexible Nonlinear Diffusion Acceleration. At each NDA iteration, the streaming and collision operator of the S{sub N} equations are (approximately) inverted using a transport sweep. When executed on multiple processors parallel block Jacobi (PBJ) splitting is utilized lagging the processor sub-domain's incoming angular fluxes making the implemented method asynchronous, i.e. the convergence properties of NDA become dependent on the number of concurrent tasks and details of the partitioning. Within this work, we study the NDA convergence properties for the two-dimensional C5G7 benchmark problem PBJ with p = 1, 2, 4, 8, 12, 16, 24, 32, 48, 60, 72, 96 and 144 concurrent tasks. Rosa studied the convergence properties of PBJ splitting methods with and without transport synthetic acceleration (TSA) in slab geometry and two-dimensional Cartesian geometry, respectively. Rosa's iteration scheme lags both the incoming angular fluxes and the scattering source making it very similar to the method described here. Rosa found by means of Fourier analysis that convergence of unaccelerated PBJ can degrade for optically thin subdomains, i.e. for a large number of processors given a fixed domain size. Depending on the choice of parameters application of TSA can lead to an effective algorithm. In contrast to Rosa's work, this work focuses on PBJ splitting for NDA accelerated solution of the multigroup eigenvalue problem. Later, Zerr and Anistratov used their integral transport matrix method in conjunction with PBJ. This iteration scheme is different as it does not lag the scattering source. Nevertheless, Fourier analysis with Diamond Difference spatial discretization showed that the method degrades with increasing the overall size of the spatial domain while keeping the sub-domain size constant. In the case of an infinite medium, the observed spectral radius becomes unity. These references establish the iterative performance of PBJ for one-group fixed source problems discretized on rectangular cells, but for the Rattlesnake first order NDA method, an emphasis lies on multigroup eigenvalue problems. In this setting, the additional complication arises that the low order equations are not exactly inverted, but only to some iterative criterion. Further, as the low order problem is solved using Jacobian-Free Newton Krylov methods, a suitable preconditioner for the GMRES iterations is required. As the effectiveness of the preconditioners may decrease when more concurrent processes are used, we expect the low order solve to impact the overall effectiveness of the NDA method in parallel execution as well. Therefore, this work focuses on the question of how detrimental the asynchronicity of the high and low order iterative solutions is for the effectiveness of NDA solutions of realistic, unstructured grid, multigroup eigenvalue problems. The iterative convergence properties of Rattlesnake's NDA method for multigroup eigenvalue problems are studied for varying number of concurrent processes. Rattlesnake's NDA method is asynchronous because the high order transport sweep uses PBJ splitting and because the low order solve's preconditioners, algebraic multigrid and additive Schwarz, are asynchronous. We found that up to 144 processes the number of Picard iterations increases by a factor of 2-3 affecting but not destroying NDA's parallel performance for the C5G7 benchmark problem, a representative LWR (light water reactor) configuration. The solution of the NDA low order eigenvalue problem posed greater problems than expected for the solvers currently available in Rattlesnake mainly because of problems to effectively precondition the modified low-order problem. As a matter of fact, the low order problem becomes an advection-diffusion problem. Non-robustness was observed for the AMG preconditioned coarse mesh acceleration for more than 60 concurrent processes, which was fixed by increasing the number of permissible V-cycles per AMG call. For fine mesh acceleration AMG proved to be ineffective and we resorted to ASM. For both AMG and ASM, increasing number of linear iterations per nonlinear are observed when increasing the number of processes, but for ASM this problem appears to be worse. The results from this work also indicate that initial development efforts should be diverted from implementation of a high-order parallel sweeping algorithm to the effective and robust iterative solution of the low order NDA multigroup eigenvalue problem. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Polarimetric ISAR: Simulation and image reconstruction

In polarimetric ISAR the illumination platform, typically airborne, carries a pair of antennas that are directed toward a fixed point on the surface as the platform moves. During platform motion, the antennas maintain their gaze on the point, creating an effective aperture for imaging any targets near that point. The interaction between the transmitted fields and targets (e.g. ships) is complicated since the targets are typically many wavelengths in size. Calculation of the field scattered from the target typically requires solving Maxwell’s equations on a large three-dimensional numerical grid. This is prohibitive to use in any real-world imaging algorithm, so the scattering process is typically simplified by assuming the target consists of a cloud of independent, non-interacting, scattering points (centers). Imaging algorithms based on this scattering model perform well in many applications. Since polarimetric radar is not very common, the scattering model is often derived for a scalar field (single polarization) where the individual scatterers are assumed to be small spheres. However, when polarization is important, we must generalize the model to explicitly account for the vector nature of the electromagnetic fields and its interaction with objects. In this note, we present a scattering model that explicitly includes the vector nature of the fields but retains the assumption that the individual scatterers are small. The response of the scatterers is described by electric and magnetic dipole moments induced by the incident fields. We show that the received voltages in the antennas are linearly related to the transmitting currents through a scattering impedance matrix that depends on the overall geometry of the problem and the nature of the scatterers.

42 ENGINEERING↗