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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Efficient shallow Ritz method for 1D diffusion problems

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].

Diffusion problems↗
DOE OSTI2024

Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

Here, in this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

early-time solution↗
DOE OSTI2025

A three-dimensional laser ray-tracing methodology for radiation-hydrodynamics simulations

We report on a methodology for performing laser ray-tracing in three spatial dimensions for radiation-hydrodynamics simulation codes. Our method, which is an extension of that developed in Haines et al., Comput. Fluids 201, 104478 (2020), utilizes an automatically generated separate mesh for the laser ray-tracing from the radiation-hydrodynamics mesh. This enables the laser mesh to be tailored to minimize ray noise with significantly fewer rays than would be required when the ray-tracing is performed on the radiation-hydrodynamics mesh, primarily by allowing the use of high-aspect-ratio cells that are not suitable for hydrodynamics solvers. For a planar target, we show that our method provides a ≈ 100× reduction in computational expense to achieve a fixed level of ray noise relative to ray-tracing directly on the radiation-hydrodynamics mesh. The relatively low ray requirement also enables efficient computation of cross-beam energy transfer. Each cell in the logically cubic laser mesh is a non-convex dodecahedron with triangular sides, and numerical integration of the ray trajectories and inverse bremsstrahlung is performed by mapping each cell to the unit cube. We will describe our methodology in detail as well as its implementation in the xRAGE radiation-hydrodynamics code, discuss performance, and present the results from applying the methodology to test problems with analytic solutions for laser ray-tracing through a quadratic density gradient with an analytic solution as well as for a laser-driven heat front. In 3D radiation-hydrodynamics simulations of laser-driven experiments performed on the National Ignition Facility, laser ray-tracing with our methodology uses less than 1% of total computational time while introducing acceptably low levels of ray noise.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Temperature of a tungsten spallation target

We discuss the heat load inside a neutron spallation target made of tungsten hit by an 800 MeV proton beam. This problem is important for the Neutron Target project, where a spallation target will be surrounded by an extended graphite or beryllium cube to create a neutron target. The idea of a free-neutron target enables the measurement of neutron-induced reactions in inverse kinematics. This idea is part of the LANSCE strategy to stay a worldwide leader for neutron-induced research.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Prediction of neutron production and energy spectrum by the inverse kinematic reaction between an incident 7 Li 3+ beam and a proton target in PHITS

A neutron source using the inverse kinematic reaction between lithium and proton, p( 7 Li, n) 7 Be, achieves forward-directed neutrons, potentially enhancing neutron yield in the forward direction. Despite the advantage, no evaluated-cross-section data for this reaction can be used in Monte Carlo simulation codes, such as PHITS. To solve this problem, this study aims to evaluate the applicability of the user-defined cross-section data, Frag data, for p ( 7 Li, n) 7 Be in PHITS. The simulations reproduced collisions between 7 Li 3+ ions and polypropylene targets. The Frag data was edited based on the JENDL-5 by utilizing the two-body collision kinematics. The neutron yield and angular distribution were investigated in the simulation. As a result, the forward neutron convergence with a reasonable neutron yield and energy spectrum was observed. The expected neutron yield in the forward 1-steradian area is 2.46 × 10 10 n/s when lithium-ion energy and current are 16.45 MeV and 0.1 mA.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Beam focusing and consequences for Doppler backscattering measurements

The phenomenon of focusing of microwave beams in a plasma near a turning-point caustic is discussed by exploiting the analytical solution to the Gaussian beam-tracing equations in the two-dimensional (2-D) linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. This focusing must be taken into account to interpret Doppler backscattering (DBS) measurements. We find that the filter function that characterises the scattering intensity contribution along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering from the beam focusing region. We show that the DBS signal enhancement for decreasing incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering, as was originally proposed by (Gusakov et al., (Plasma Phys. Contr. Fusion, vol. 56, 2014, p. 0250092014, 2017); Plasma Phys. Rep. vol. 43(6), 2017, pp. 605–613). The analytic beam model is used to predict the measurement of the k y density-fluctuation wavenumber power spectrum via DBS, showing that, in an NSTX-inspired example, the spectral exponent of the turbulent, intermediate-to-high k y density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Polynomial-time preparation of low-temperature Gibbs states for two-dimensional toric code

In this work, we propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial state, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. We prove that fast mixing at low temperature for the two-dimensional toric code can be achieved by augmenting local jump operators with simple global jump operators, which enable efficient transitions between logical sectors. To establish tight lower bounds on the spectral gap, we introduce a new reduction method that eventually maps the problem to estimating the spectral gap of a perturbed graph Laplacian on a stair graph. Our proof also shows that the Lindblad dynamics with a digitally implemented low-temperature local Davies generator is able to efficiently drive the quantum state toward the ground state manifold.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Electromagnetic energy calibration of the SoLid detector with horizontal muons

SoLid is a neutrino experiment at very-short baselinesearching for active-to-sterile oscillations of reactorantineutrinos. The detection principle is based on the pairing oftwo types of solid scintillators: polyvinyl toluene and $^{6}$Li:ZnS(Ag), which is a new technology used in this field ofPhysics. In addition to good neutron-gamma discrimination, thissetup allows the detector to be highly segmented; the basicdetection unit is a 5 cm cube. High segmentation provides numerousadvantages including precise localisation of the Inverse Beta Decay(IBD) products, the derivation of an antineutrino energy estimatorbased on the isolated positron energy, and a powerful backgroundreduction tool that relies on the topological signature of thesignal. Finally, the system is read out by a network ofwavelength-shifting fibres coupled to photosensors. A relativeelectromagnetic calibration is performed with horizontal cosmicmuons. This source poses the simplest calibration problem in which asingle detection unit is involved. In addition, large muon energydeposits allow us to perform a calibration at the most detailedlevel (i.e. per fibre) and to accurately define the fraction ofenergy escaping to neighbouring detection cells. A statisticalprecision at the sub-percent level is reached. The paper alsodiscusses two methods to calibrate the absolute energy scale andpresents their implementation and results. The first method relieson horizontal muons, though the precision is limited to around 10%because of the uncertainty in the energy distribution of suchmuons. A novel, alternative method based on the radioactiveamericium-beryllium source is proposed. It takes advantage of theelectron-positron pair-production process and provides a calibrationpoint at 3.4 MeV (i.e. in the core of the IBD positronspectrum). The paper is concluded with various cross-check includinga determination of the energy spectrum of the standard cosmogenicbackground candle: $^{12}$B.

Abreu, Y. [Antwerp U.]↗
DOE OSTI2024

(Doublon) Benchmarking of Different Inverse Point Kinetics Implementations for an Autocorrected Reactimeter Algorithm

In November 2017, the Transient Reactor Test Facility returned to operation. Since that time, many transient test series have been completed, such as the Transient Heatsink Overpower Response capsule (THOR), the Transient Water Irradiation System for TREAT (TWIST), and Sirius. Each has provided valuable data for materials performance and reactor safety that can be applied in future designs. During each experimental series, detector count rates provided important information on the core behavior during transients. However, a limitation of these data is that variations in the neutron distribution during experiments can cause errors when attempting to infer reactivity evolution from detector signals. Neutron physics codes can be used to compute the flux shape variations. However, this is a poor solution when the experimental data is used for code verification, validation and uncertainty quantification. Indeed, if the output of the code is used both as a reference and to correct what the reference is compared to, the circular dependency limits the quality of the verification, validation and uncertainty quantification approach. To overcome this problem, the autocorrected reactimeter algorithm (ACRA) has been developed. This approach infers a time-dependent reactivity evolution by testing different spatial corrections and selecting the one that minimizes reactivity variations when the core is in a frozen configuration (i.e., when there is no variation in parameters affecting reactivity). However, the scope of this method was limited to transients where there were negligible thermal feedback. Indeed, the core is never in a frozen configuration when the fuel temperature varies during the whole transient. This is our motivation for developing an improved version of the ACRA that does not require frozen configurations. To develop this new algorithm, we need a precise and unbiased implementation of the inverse point kinetic equations (IPKEs) as any error in the reactivity evaluation will be propagated into the choice of the optimal spatial correction. Indeed, the previous reactimeter algorithm would use approximations, such as a negligible flux amplitude derivative, to focus on rapidity. For the numerical validation of ACRA, we aim at absolute error under for reactivity derived from signals similar to the one of this study. In this summary, we test eight different IPKE implementations. Each will process a mockup signal built for this study, similar to those that the future ACRA will process. Each reactivity output will be compared to the reference reactivity that has been used to generate the mockup signal. The implementation minimizing the difference with the reference reactivity will be used in the development of a new ACRA formulation.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

A Discrete Hankel Transform Approach to Nuclear Data Processing for Fusion Applications

This study introduces advancements to the numerical solutions employed in the processing of nuclear data for fusion applications. It leverages the convolution theorem and Fourier transform techniques to enhance computational efficiency and broaden applicability. Building upon a previously reported discrete Hankel transform approach for Doppler broadening, this work refines the solution of convolution integrals central to these applications. The methodology provides a general and unified framework for evaluating any convolution operation, regardless of whether the underlying problem involves temperature effects in nuclear reactions. The applicability to the nuclear data processing for fusion is demonstrated by deriving the convolution integrals for some of the fusion-related quantities. As before, the convolution operation utilizes a Gaussian-based kernel; however, the discrete Hankel transform of order $𝛼$ = $\frac{1}{2}$ is now applied to the forward Fourier transform of the nonkernel argument, rather than the inverse Fourier transform. This modification eliminates the need for the integration of the nonkernel, cross section–based function, which is a step that posed challenges for certain pointwise cross-section representations. It also removes the requirement for cross-section linearization. Optimized for graphics processing unit architectures, the approach significantly improves computational performance. These advancements are currently under evaluation as the foundation for the next-generation thermonuclear data file processing codes being developed at Lawrence Livermore National Laboratory.

Nuclear science and engineering↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Explicit block encodings of boundary value problems for many-body elliptic operators

Simulation of physical systems is one of the most promising use cases of future digital quantum computers. In this work we systematically analyze the quantum circuit complexities of block encoding the discretized elliptic operators that arise extensively in numerical simulations for partial differential equations, including high-dimensional instances for many-body simulations. When restricted to rectangular domains with separable boundary conditions, we provide explicit circuits to block encode the many-body Laplacian with separable periodic, Dirichlet, Neumann, and Robin boundary conditions, using standard discretization techniques from low-order finite difference methods. To obtain high-precision, we introduce a scheme based on periodic extensions to solve Dirichlet and Neumann boundary value problems using a high-order finite difference method, with only a constant increase in total circuit depth and subnormalization factor. We then present a scheme to implement block encodings of differential operators acting on more arbitrary domains, inspired by Cartesian immersed boundary methods. We then block encode the many-body convective operator, which describes interacting particles experiencing a force generated by a pair-wise potential given as an inverse power law of the interparticle distance. This work provides concrete recipes that are readily translated into quantum circuits, with depth logarithmic in the total Hilbert space dimension, that block encode operators arising broadly in applications involving the quantum simulation of quantum and classical many-body mechanics.

Kharazi, Tyler [University of California, Berkeley↗
DOE OSTI2025

Describing hadronization via histories and observables for Monte-Carlo event reweighting

We introduce a novel method for extracting a fragmentation model directly from experimental data without requiring an explicit parametric form, called Histories and Observables for Monte-Carlo Event Reweighting (HOMER), consisting of three steps: the training of a classifier between simulation and data, the inference of single fragmentation weights, and the calculation of the weight for the full hadronization chain. We illustrate the use of HOMER on a simplified hadronization problem, a q\bar{q} q q ‾ string fragmenting into pions, and extract a modified Lund string fragmentation function f(z) f ( z ) . We then demonstrate the use of HOMER on three types of experimental data: (i) binned distributions of high-level observables, (ii) unbinned event-by-event distributions of these observables, and (iii) full particle cloud information. After demonstrating that f(z) f ( z ) can be extracted from data (the inverse of hadronization), we also show that, at least in this limited setup, the fidelity of the extracted f(z) f ( z ) suffers only limited loss when moving from (i) to (ii) to (iii). Public code is available at https://gitlab.com/uchep/mlhad.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Signature of Correlated Insulator in Electric Field Controlled Superlattice

On a two-dimensional crystal, a “superlattice” with nanometer-scale periodicity can be imposed to tune the Bloch electron spectrum, enabling novel physical properties inaccessible in the original crystal. While creating 2D superlattices by means of nanopatterned electric gates has been studied for band structure engineering in recent years, evidence of electron correlations-which drive many problems at the forefront of physics research-remains to be uncovered. Here, in this work, we demonstrate signatures of a correlated insulator phase in Bernal-stacked bilayer graphene modulated by a gate-defined superlattice potential, manifested as resistance peaks centered at integer multiples of single electron per superlattice unit cell carrier densities. The observation is consistent with the formation of a stack of flat low-energy bands due to the superlattice potential combined with inversion symmetry breaking. Our work paves the way to custom-designed superlattices for studying band structure engineering and strongly correlated electrons in 2D materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Bayesian Analysis of TRISO Fuel: Quantifying Model Inadequacy, Incorporating Lower-Length-Scale Effects, and Developing Parallel Active Learning Capabilities

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel-cycle systems. This program has been providing engineering-scale support for the continued development of BISON, a high-fidelity, high-resolution fuel performance tool. Fuel behavior in nuclear reactors is governed by a complex network of mechanisms that interact with various other physics aspects in the reactor system. Any model developed to represent fuel behavior will likely be idealized, resulting in uncertainties when comparing their predictions against the observed data. In Fiscal Year (FY)-23, we initiated the Uncertainty Quantification (UQ) work by using Bayesian methods to establish a level of model trustworthiness and further improve it, with a particular emphasis on TRI-Structural isOtropic (TRISO) nuclear fuel. This year, we further expanded on that UQ work by investigating an approach to quantifying model inadequacy and accounting for lower-length scale (LLS) effects in TRISO silver (Ag) release modeling. Furthermore, we are implementing parallel active learning capabilities to reduce the computational cost (i.e., required computational resources and elapsed time) of performing UQ. Specifically, we utilized The Kennedy O’Hagan framework for Bayesian uncertainty quantification (KOH) to account for model inadequacy in TRISO Ag release predictions made by BISON. The KOH framework represents an improvement over the standard Bayesian framework used in FY-23. Explicitly accounting for model inadequacy in the Bayesian framework helps establish the level of experimental noise uncertainty in the Advanced Gas Reactor (AGR) data. We compared the inverse UQ results obtained from both the standard Bayesian and KOH frameworks in light of the AGR-2/3/4 data, and also compared the predictive UQ results obtained from these two frameworks in light of the AGR-1 data. Next, we investigated the impact of considering LLS effects in the Ag release simulations. We developed an expanded database of LLS simulated effective diffusivities for Ag, covering a wide range of microstructures and temperatures. Using this database, we developed a framework for incorporating LLS effects into the engineering-scale Ag release UQ. We developed both parametric and non-parametric approaches for bridging the length scales. We then investigated the inverse UQ results in light of the AGR-2/3/4 data and the predictive UQ results in light of the AGR-1 data, and compared the LLS-informed approach and the Arrhenius equation, which does not include microstructure information. Finally, we discussed implementing parallel active learning capabilities in the Multiphysics Object Oriented Simulation Environment (MOOSE)/BISON to reduce the computational cost (i.e., computational resources and elapsed time) of Bayesian UQ. For verification purposes, we first tested these new capabil ities on a species interaction problem. We then demonstrated them on the TRISO Ag release application, showing that parallel active learning capabilities can enhance the accuracy of UQ while also substantially reducing the computational cost in comparison to the reference methods developed in FY-23.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

LuGo: An enhanced quantum phase estimation implementation

Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard implementation of QPE faces challenges related to time complexity and circuit depth, which limit its practicality for large-scale computations. We introduce LuGo, a novel framework designed to enhance the performance of QPE by reducing circuit duplication, as well as using parallelization techniques to achieve faster generation of the QPE circuit and gate reduction. We validate the effectiveness of our framework by generating quantum linear solver circuits, which require both QPE and inverse QPE, to solve linear systems of equations. LuGo achieves significant improvements in both computational efficiency and hardware requirements without compromising on accuracy. Compared to a standard QPE implementation, LuGo reduces time consumption to generate a circuit that solves a 2 6 × 2 6 system matrix by a factor of 50.68 and over 31× reduction of quantum gates and circuit depth, with no fidelity loss on an ideal quantum simulator. Furthermore, we demonstrated the versatility and scalability of LuGo enabled HHL algorithm by simulating a canonical Hele-Shaw fluid problem using a quantum simulator. With these advantages, LuGo paves the way for more efficient implementations of QPE, enabling broader applications across several quantum computing domains.

Quantum algorithm↗
DOE OSTI2025

Sequential spectral line analysis for accurate density and temperature diagnosis of laboratory opacity measurements

The accuracy of iron opacity calculated in stellar interiors has been questioned since the discovery of the “solar problem” and the discrepancies between the measured and modeled iron opacity reported in 2015. Experimental opacity benchmarks require accurate temperature and density measurements, which were inferred by analyzing tracer magnesium spectra in those experiments. Could the observed discrepancy be explained by insufficient accuracy in the inferred temperature, density, and their uncertainties? Previous analyses may have yielded biased results due to three limitations: (1) simultaneous multi-line fitting, (2) approximations in line-shape models, and (3) exclusion of certain spectral lines due to insufficient background characterization. Notably, the first issue is a common concern for many inversion methods, including Bayesian inferences. We present a refined analysis method that overcomes these limitations, applied to three categories of iron opacity experiments (Anchor 1, 2, and 3). In particular, the sequential fitting method yields unbiased results with more realistic uncertainties by accounting for line inconsistencies in the parameter uncertainties. The average electron temperature and density values are 162 ± 6 eV and (7.0 ± 1.9) × 10 21 cm −3 for six Anchor 1 experiments, 189 ± 7 eV and (3.4 ± 0.3) × 10 22 cm −3 for 21 Anchor 2 experiments, and 201 ± 6 eV and (4.8 ± 1.1) × 10 22 cm −3 for nine Anchor 3 experiments. These results show ∼4% temperature and ∼20% density reproducibility over a decade, which also aligns with the inferred parameter uncertainties. In conclusion, the resulting temperature and density uncertainties lead to a quasi-continuum iron opacity variation of ±4%–7% for wavelengths below 9.5 Å, which is insufficient to explain the significant model-data discrepancies reported in 2015.

Absorption spectroscopy↗
DOE OSTI2024

ML Classifier Fusion for Three Data Streams with Quality Inversely Proportional to Time Resolution

We consider a monitoring scenario of phenomenon using three different streams of measurements whose quality is proportional to their constant inter-arrival times. Each measurement of a stream needs to be binary-classified to reflect the state of interest of the phenomenon. A set of classifiers is separately trained and fused for each stream at its time resolution using measurements collected under known states. We present a machine learning method to fuse the outputs of these fusers to provide a final classification at the finest time resolution. We show that this fused-fusers method provides decisions with likely superior classification probability compared to the best individual classifiers and fused-classifiers. We derive generalization equations that guarantee a superior classification probability of fused-fusers with a confidence probability specified by the classifiers’ generalization equations. We apply these results to study a practical problem of classifying Pu/Np target dissolution events at a radiochemical processing facility using gamma spectral measurements of effluent flows.

Rao, Nageswara↗