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DOE OSTI2021

Neutrino-assisted early dark energy: theory and cosmology

Abstract The tension between measurements of the Hubble constant obtained at different redshifts may provide a hint of new physics active in the relatively early universe, around the epoch of matter-radiation equality. A leading paradigm to resolve the tension is a period of early dark energy, in which a scalar field contributes a subdominant part of the energy budget of the universe at this time. This scenario faces significant fine-tuning problems which can be ameliorated by a non-trivial coupling of the scalar to the standard model neutrinos. These become non-relativistic close to the time of matter-radiation equality, resulting in an energy injection into the scalar that kick-starts the early dark energy phase, explaining its coincidence with this seemingly unrelated epoch. We present a minimal version of this neutrino-assisted early dark energy model, and perform a detailed analysis of its predictions and theoretical constraints. We consider both particle physics constraints — that the model constitute a well-behaved effective field theory for which the quantum corrections are under control, so that the relevant predictions are within its regime of validity — and the constraints provided by requiring a consistent cosmological evolution from early through to late times. Our work paves the way for testing this scenario using cosmological data sets.

Astronomy & Astrophysics↗

DOE OSTI2021

On Distributed Model-Free Reinforcement Learning Control with Stability Guarantee

Distributed learning can enable scalable and effective decision making in numerous complex cyber-physical systems such as smart transportation, robotics swarm, power systems, etc. However, the stability of the system is usually not guaranteed in most existing learning paradigms; and this limitation can hinder the wide deployment of machine learning in decision making of safety-critical systems. This paper presents a stability guaranteed distributed reinforcement learning (SGDRL) framework for interconnected linear subsystems, without knowing the subsystem models. While the learning process requires data from a peer-to-peer (p2p) communication architecture, the control implementation of each subsystem is only based on its local state. The stability of the interconnected subsystems will be ensured by a diagonally dominant eigenvalue condition, which will then be used in a model-free RL algorithm to learn the feedback control gains. The RL algorithm structure follows an off-policy iterative framework, with interleaved policy evaluation and policy update steps. We numerically validate our theoretical results by performing simulations on four interconnected sub-systems.

Mukherjee, Sayak↗

DOE OSTI2026

The emergent photophysics and photochemistry of molecular polaritons: a theoretical and computational investigation (Final Technical Report)

When molecules are placed between closely spaced mirrors, they interact strongly with the photons that are trapped between them, generating new quantum states which are no longer exclusively material nor photonic alone, but rather, coherent superpositions of both. These hybrid states are known as molecular polaritons, given that they arise from the strong interaction between the electric field of light and the electrical polarization of the molecules. Recently, experimental advances in nano‐ and microfabrication of molecular polariton architectures have successfully demonstrated their feasibility to control the rate and outcome of a certain class of chemical reactions in condensed phases. Importantly, these reactions proceed in strongly dissipative environments such as liquid solvents and lossy mirrors that allow for photons to escape from their confinement. The purpose of this research is to formulate quantum mechanical theories and computational tools that can elucidate the origin of these intriguing phenomena and simultaneously predict capabilities that this new generation of molecular materials affords. Attention is placed on harnessing polaritons to carry out photophysics and photochemistry that challenge currently existing paradigms, such as the optimization of energy conversion processes in organic solar cell or light‐emitting devices, or unconventional phenomena such as long‐range excitation energy transfer, remote control of chemical reactions, and a new quantum mechanical regime of chemical reactivity due to wavefunction overlaps amongst a large number of molecular polaritons (Bose condensation). This research explores a frontier of Chemistry and Physics where electrons, vibrations, and photons interact strongly with each other to generate emergent behavior that can be creatively exploited to address contemporary challenges in Basic Energy Sciences.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2009

Halophytes, Algae, and Bacteria Food and Fuel Feedstocks

The constant, increasing demand for energy, freshwater, and food stresses our ability to meet these demands within reasonable cost and impact on climate while sustaining quality of life. This environmental Triangle of Conflicts between energy, food, and water--while provoked by anthropogenic monetary and power struggles--can be resolved through an anthropogenic paradigm shift in how we produce and use energy, water, and food. With world population (6.6 billion) projected to increase 40 percent in 40 to 60 yr, proper development of saline agriculture and aquaculture is required, as 43 percent of the Earth's landmass is arid or semi-arid and 97 percent of the Earth's water is seawater. In light of this, we seek fuel alternatives in plants that thrive in brackish and saltwater with the ability to survive in arid lands. The development and application of these plants (halophytes) become the primary focus. Herein we introduce some not-so-familiar halophytes and present a few of their benefits, cite a few research projects (including some on the alternatives algae and bacteria), and then set theoretical limits on biomass production followed by projections in terms of world energy demands. Based on diverse arid lands with a total size equivalent to the Sahara Desert (8.6(exp 8) ha, or 2.1(exp 9) acres), these projections show that halophyte agriculture and algae systems can provide for the projected world energy demand.

Hendricks, R. C.↗

DOE OSTI2022

Iron pnictides and chalcogenides: a new paradigm for superconductivity

Superconductivity is a remarkably widespread phenomenon observed in most metals cooled down to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the celebrated Bardeen Cooper-Schrieffer (BCS) theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in new and unexpected ways. In the case of the iron-based superconductors, this includes a new appreciation of the ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. Besides superconductivity, these materials have also led to new insights into the unusual metallic state governed by the Hund’s interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the significance of topology in correlated states. Furthermore, over the thirteen years since their discovery, they have proven to be an incredibly fruitful testing ground for the development of new experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

The importance of maldistribution matching for thermal performance of compact heat exchangers

Compact heat exchangers have gained increased attention in recent years, particularly in demanding applications where high temperatures, high pressures, and/or high power densities are required. For decades, the heat exchanger (HX) community believes that flow maldistribution is a key factor for HX effectiveness, that is, reducing the degree of flow maldistribution (MALD) can help increase the HX effectiveness. Therefore, significant efforts have been devoted in the past to optimizing the header geometry to minimize flow maldistribution. This work was initially motivated by this, and the original goal was to figure out a HX header design with the lowest maldistribution. However, by systematically constructing a comprehensive maldistribution matrix, the analysis revealed that the HX effectiveness is not actually determined by the MALD, but instead dominated by the degree of maldistribution mismatch (MISM). This conclusion was also theoretically generalized, which indicated that matching of the local heat capacity rate is key for achieving maximum performance. The MISM provides a local means of tracking this information, while the MALD only provides a global approximation of the maldistribution itself. With this new perspective, flow maldistribution needs not necessarily be avoided, but instead matched between two fluid streams, to improve the HX performance. We demonstrated that by carefully designing the header geometry to match the velocity profiles of the two fluids in a 2 MW PCHE with molten salt and supercritical carbon dioxide (sCO2) as the heat transfer fluids, the HX could achieve a higher effectiveness even when the maldistribution increased. Finally, a technoeconomic study using a CSP system as an example revealed that the use of this new HX design paradigm could result in CSP capital cost savings as large as 16.6%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2023

Standard experimental paradigm designs and data exclusion practices in cognitive psychology can inadvertently introduce systematic “shadow” biases in participant samples

Abstract Standard cognitive psychology research practices can introduce inadvertent sampling biases that reduce the reliability and generalizability of the findings. Researchers commonly acknowledge and understand that any given study sample is not perfectly generalizable, especially when implementing typical experimental constraints (e.g., limiting recruitment to specific age ranges or to individuals with normal color vision). However, less obvious systematic sampling constraints, referred to here as “shadow” biases, can be unintentionally introduced and can easily go unnoticed. For example, many standard cognitive psychology study designs involve lengthy and tedious experiments with simple, repetitive stimuli. Such testing environments may 1) be aversive to some would-be participants (e.g., those high in certain neurodivergent symptoms) who may self-select not to enroll in such studies, or 2) contribute to participant attrition, both of which reduce the sample’s representativeness. Likewise, standard performance-based data exclusion efforts (e.g., minimum accuracy or response time) or attention checks can systematically remove data from participants from subsets of the population (e.g., those low in conscientiousness). This commentary focuses on the theoretical and practical issues behind these non-obvious and often unacknowledged “shadow” biases, offers a simple illustration with real data as a proof of concept of how applying attention checks can systematically skew latent/hidden variables in the included population, and then discusses the broader implications with suggestions for how to manage and reduce, or at a minimum acknowledge, the problem.

Siritzky, Emma M.↗

DOE OSTI2025

Tunable magnons of an antiferromagnetic Mott insulator via interfacial metal-insulator transitions

Antiferromagnetic insulators present a promising alternative to ferromagnets due to their ultrafast spin dynamics essential for low-energy terahertz spintronic device applications. Magnons, i.e., quantized spin waves capable of transmitting information through excitations, serve as a key functional element in this paradigm. However, identifying external mechanisms to effectively tune magnon properties has remained a major challenge. Here we demonstrate that interfacial metal-insulator transitions offer an effective method for controlling the magnons of Sr 2 IrO 4 , a strongly spin-orbit coupled antiferromagnetic Mott insulator. Resonant inelastic x-ray scattering experiments reveal a significant softening of zone-boundary magnon energies in Sr 2 IrO 4 films epitaxially interfaced with metallic 4 d transition-metal oxides. Therefore, the magnon dispersion of Sr 2 IrO 4 can be tuned by metal-insulator transitions of the 4 d transition-metal oxides. We tentatively attribute this non-trivial behavior to a long-range phenomenon mediated by magnon-acoustic phonon interactions. Our experimental findings introduce a strategy for controlling magnons and underscore the need for further theoretical studies to better understand the underlying microscopic interactions between magnons and phonons.

magnetic properties and materials↗

DOE OSTI2026

A roadmap toward scaling, reasoning and self-evolving foundation models for nuclear and particle physics

Foundation models have revolutionized artificial intelligence, with Large Language Models demonstrating unprecedented capabilities in multimodal understanding, reasoning and tool use. Nuclear and particle physics stands at a critical juncture where similar transformative potential awaits realization. The field generates exabytes of experimental data, exascale simulations, and decades of theoretical insights — yet these remain largely disconnected from modern Artifical Intelligence (AI) capabilities, with most physics AI applications confined to narrow, task-specific models that suffer from domain shifting when applied to real experimental data. We present a roadmap for FM4NPP (Foundation Model for Nuclear and Particle Physics), systematically scaling from current proof-of-concept models to trillion-parameter architectures capable of autonomous discovery. Our approach advances three critical frontiers: unified data infrastructure integrating detector data, scientific knowledge and computational tools across global facilities; multi-facility foundation models enabling cross-experiment knowledge transfer and accelerated discovery; and agentic AI capabilities for reasoning and autonomous tool use. The resulting self-evolving FM4NPP will transform physics research by converting time-intensive data analysis, theory derivation and computational bottlenecks into rapid AI–human collaborative discovery. This paradigm shift promises to fundamentally accelerate scientific progress in nuclear and particle physics, enabling researchers to focus on high-level insights while AI handles routine analysis and explores vast parameter spaces beyond human capacity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Thermal coupling-decoupling mechanism of heat transfer across van der Waals interfaces in n-eicosane

Progress toward improving thermal transport properties of n-eicosane, a promising phase change material for thermal energy storage near human body temperature, is hindered by lack of a general theoretical framework to model thermal interfacial conductance (TIC) of the van der Waals (vdW) force bonded molecular interfaces, which have little compositional/structural mismatch. Combining molecular dynamics simulations at temperatures up to the melting point and a time-domain analysis of interfacial heat currents in individual molecules, we unveil that (1) the heat flux across a molecular vdW interface has an alternating coupling-decoupling pattern at the single molecule level due to thermal fluctuations, and (2) the net heat transfer during the thermally coupled periods is orders of magnitude larger than that during the thermally decoupled periods. Furthermore, we demonstrate that a vdW interface's TIC correlates almost linearly with two atomistic-scale coupling-decoupling parameters: αc and σc, that represent the duration and strength of the thermal coupling, respectively. This thermal coupling-decoupling mechanism proposes a new paradigm that explicitly accounts for the effects of structural flexibility and dynamical fluctuation on heat transfer across molecular interfaces, and will likely provide new insights into modeling thermal transport properties in a wide-ranging soft materials, including self-assembled monolayers, paraffins or lipids.

42 ENGINEERING↗

DOE OSTI2024

Provable bounds for noise-free expectation values computed from noisy samples

Quantum computing has emerged as a powerful computational paradigm capable of solving problems beyond the reach of classical computers. However, today’s quantum computers are noisy, posing challenges to obtaining accurate results. Here, we explore the impact of noise on quantum computing, focusing on the challenges in sampling bit strings from noisy quantum computers and the implications for optimization and machine learning. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the conditional value at risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on real quantum computers involving up to 127 qubits. The results show strong alignment with theoretical predictions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Developing Mars-Based Clinical Scenarios for an Earth Independent Medical Operations (EIMO) – Based Decision Support Service

As crewed missions move beyond Low-Earth Orbit, pre-mission planning cannot fully buy down the medical risks of exploration-class missions. Martian missions, where increased hazards exist, (such as long-duration spaceflight, surface-level EVA operations, and communications delays) will require a paradigm shift in the structure of a medical system. An Earth-Independent Medical Operations-based Medical System (EIMO-MS) will need to optimize four critical domains to help provide medical care: utilization of Pre-Mission Planning, augmentation of Acute and Prolonged Medical Decision Making, automated tracking of Resource Management, and assistance in Task Load Balance. The ideal EIMO-MS will be able to accomplish this goal by having an interactive, adaptable interface that will be able to provide real-time medical services. It must respond based on the level of crewmember training, medical situation, and available medical and non-medical resources. To showcase the capabilities and requirements of such a sophisticated automated MS, a series of clinical scenarios of escalating complexity were developed with clinical and systems engineering input. These scenarios describe in clinical detail what a theoretical future medical system, enhanced with multiple information streams (such as a medical database, an AI-based Decision Support System, real-time monitoring, enhanced in-situ laboratory imaging, etc.) can achieve in conjunction with a trained and experienced crew. Scenarios are comprised of: a context section including objectives and applicable spaceflight environment, a highlighted assumptions section, a clinical narrative section, and a systems engineering activity diagram demonstrating the integrated Medical System (MS). The “swim lanes” of the activity diagram act as the logistical core of each scenario and show how the MS will interact with the crew, ground support, and other in-flight systems. The Design Reference Mission that is used for the scenarios is based on existing reference mission profiles [1] with a projected 30-sol stay on the Martian surface. Scenarios span the spectrum from planned evaluations, minor medical care, urgent care, surgical guidance, critical and expectant management, and behavioral health care. Mission complexity will exponentially increase during deep space and Mars exploration-class missions, and medical support for these missions will likewise need to increase in autonomy and adaptability. The integrated system that will support these missions will need to provide assistance in a variety of anticipated and unforeseen scenarios. These medical scenarios, guided by clinician input, are initial steps in crafting the requirements for an EIMO-based medical system. By working in a systems engineering framework, requirements and capabilities can be extracted and mapped while maintaining a clinical core.

Prashant Parmar↗

DOE OSTI2026

Visualizing electronic structure of twisted bilayer MoTe 2 in devices

The pursuit of emergent quantum phenomena lies at the forefront of modern condensed matter physics. A recent breakthrough in this arena is the discovery of the fractional quantum anomalous Hall effect (FQAHE) in twisted bilayer MoTe₂ (tbMoTe₂), marking a paradigm shift and establishing a versatile platform for exploring the intricate interplay among topology, magnetism, and electron correlations. While significant progress has been made through both optical and electrical transport measurements, direct experimental insights into the electronic structure – crucial for understanding and modeling this system – have remained elusive. Here, using spatially and angle-resolved photoemission spectroscopy (μ-ARPES), we directly map the electronic band structure of tbMoTe₂. We identify the valence band maximum, whose partial filling underlies the FQAHE, at the K points, situated approximately 150 meV above the Γ valley. By fine-tuning the doping level via in-situ alkali metal deposition, we also resolve the conduction band minimum at the K point, providing direct evidence that tbMoTe₂ exhibits a direct band gap – distinct from all previously known moiré bilayer transition metal dichalcogenide systems. These results offer critical insights for theoretical modeling and advance our understanding of fractionalized excitations and correlated topological phases in this emergent quantum material.

Chen, Cheng [Univ. of Oxford (United Kingdom)]↗

DOE OSTI2021

Anomalous thermoelectricity at the two-dimensional structural transition of SnSe monolayers

The thermoelectric figure of merit ZT comprises electronic and vibrational contributions that drastically change across phase transitions, and the most common theoretical ab initio approach to thermoelectricity fails to describe the evolution of ZT across finite-temperature structural transitions in its entirety. Furthermore, while the thermoelectric behavior of bulk SnSe has been extensively studied, SnSe monolayers have been experimentally realized only recently, and the existent prediction of thermoelectricity on this two-dimensional material is unreliable because it misses its structural transition altogether. SnSe monolayers (and similar GeS, GeSe, GeTe, SnS, and SnTe monolayers) experience a temperature-induced two-dimensional Pnm2 1 → P4/nmm structural transition precipitated by the softening of vibrational modes, and we describe their thermoelectric properties across the phase transition, using molecular dynamics data to inform both electronic and vibrational coefficients directly and within the same footing. Similar to recent experimental observations pointing to an overestimated ZT past the transition temperature in bulk SnSe, we find a smaller ZT on SnSe monolayers when compared to its value predicted by the standard paradigm, due to the dramatic changes in the electrical conductivity and lattice thermal conductivity as the structural transition ensues. Here, the process described here lends a strong focus to both the vibrational and electronic evolutions throughout the structural transition, and it applies to thermoelectric materials undergoing thermally driven solid-to-solid structural phase transitions in one, two, and three dimensions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2023

Near-field terahertz nonlinear optics with blue light

Abstract The coupling of terahertz optical techniques to scattering-type scanning near-field microscopy (s-SNOM) has recently emerged as a valuable new paradigm for probing the properties of semiconductors and other materials on the nanoscale. Researchers have demonstrated a family of related techniques, including terahertz nanoscopy (elastic scattering, based on linear optics), time-resolved methods, and nanoscale terahertz emission spectroscopy. However, as with nearly all examples of s-SNOM since the technique’s inception in the mid-1990s, the wavelength of the optical source coupled to the near-field tip is long, usually at energies of 2.5 eV or less. Challenges in coupling of shorter wavelengths (i.e., blue light) to the nanotip has greatly inhibited the study of nanoscale phenomena in wide bandgap materials such as Si and GaN. Here, we describe the first experimental demonstration of s-SNOM using blue light. With femtosecond pulses at 410 nm, we generate terahertz pulses directly from bulk silicon, spatially resolved with nanoscale resolution, and show that these signals provide spectroscopic information that cannot be obtained using near-infrared excitation. We develop a new theoretical framework to account for this nonlinear interaction, which enables accurate extraction of material parameters. This work establishes a new realm of possibilities for the study of technologically relevant wide-bandgap materials using s-SNOM methods.

47 OTHER INSTRUMENTATION↗

NASA NTRS2002

Defect Localization Capabilities of a Global Detection Scheme: Spatial Pattern Recognition Using Full-field Vibration Test Data in Plates

Recently, a conceptually simple approach, based on the notion of defect energy in material space has been developed and extensively studied (from the theoretical and computational standpoints). The present study focuses on its evaluation from the viewpoint of damage localization capabilities in case of two-dimensional plates; i.e., spatial pattern recognition on surfaces. To this end, two different experimental modal test results are utilized; i.e., (1) conventional modal testing using (white noise) excitation and accelerometer-type sensors and (2) pattern recognition using Electronic speckle pattern interferometry (ESPI), a full field method capable of analyzing the mechanical vibration of complex structures. Unlike the conventional modal testing technique (using contacting accelerometers), these emerging ESPI technologies operate in a non-contacting mode, can be used even under hazardous conditions with minimal or no presence of noise and can simultaneously provide measurements for both translations and rotations. Results obtained have clearly demonstrated the robustness and versatility of the global NDE scheme developed. The vectorial character of the indices used, which enabled the extraction of distinct patterns for localizing damages proved very useful. In the context of the targeted pattern recognition paradigm, two algorithms were developed for the interrogation of test measurements; i.e., intensity contour maps for the damaged index, and the associated defect energy vector field plots.

Saleeb, A. F.↗

DOE OSTI2025

Zero Trust Strategies for Chemical, Biological, Radiological, and Nuclear Detection Systems: D.1 Cyber Scenarios

The evolving landscape of cybersecurity necessitates a paradigm shift to a Zero Trust (ZT) model, which assumes breaches and continuously verifies trust. This approach reshapes how trust boundaries are established, focusing on identities, devices, networks, applications, and data, rather than solely relying on perimeter defenses such as firewalls. Central to this transformation is the National Institute of Standards and Technology's (NIST) Special Publication 800-207, outlining the Zero Trust Architecture (ZTA), along with Executive Order 14028, which mandates federal agencies to adopt ZT principles. Complementary to these efforts, the Cybersecurity and Infrastructure Security Agency (CISA) developed the Zero Trust Maturity Model (ZTMM), providing a framework with five pillars and three cross-cutting capabilities to guide agencies toward enhanced cybersecurity maturity. In support of these initiatives, the DHS Countering Weapons of Mass Destruction Office (CWMD) is applying ZT principles to secure Chemical, Biological, Radiological, and Nuclear (CBRN) detection systems. Recognizing the diverse deployment models and network connectivity of these systems—from stationary, non-networked units to mobile, cloud-connected devices—the Pacific Northwest National Laboratory (PNNL) is developing cybersecurity scenarios specifically for CBRN environments. These scenarios examine various configurations and technological capabilities, offering insights into the application of ZTMM pillars in enhancing the security postures of CBRN devices. The cybersecurity scenarios presented by PNNL are hypothetical, crafted to explore theoretical situations and stimulate discussion on the potential use or compromise of CBRN detection systems in varied contexts. These narratives are illustrative and do not reference any real events or actual networks. Instead, they employ generalized reference models to highlight concepts and potential issues within CBRN security, focusing on how Zero Trust strategies can be adapted to address these challenges effectively.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

NASA NTRS2002

Pulsed Electromagnetic Acceleration of Plasmas

A major shift in paradigm in driving pulsed plasma thruster is necessary if the original goal of accelerating a plasma sheet efficiently to high velocities as a plasma "slug" is to be realized. Firstly, the plasma interior needs to be highly collisional so that it can be dammed by the plasma edge layer not (upstream) adjacent to the driving 'vacuum' magnetic field. Secondly, the plasma edge layer needs to be strongly magnetized so that its Hall parameter is of the order of unity in this region to ensure excellent coupling of the Lorentz force to the plasma. Thirdly, to prevent and/or suppress the occurrence of secondary arcs or restrike behind the plasma, the region behind the plasma needs to be collisionless and extremely magnetized with sufficiently large Hall parameter. This places a vacuum requirement on the bore conditions prior to the shot. These requirements are quantified in the paper and lead to the introduction of three new design parameters corresponding to these three plasma requirements. The first parameter, labeled in the paper as gamma (sub 1), pertains to the permissible ratio of the diffusive excursion of the plasma during the course of the acceleration to the plasma longitudinal dimension. The second parameter is the required Hall parameter of the edge plasma region, and the third parameter the required Hall parameter of the region behind the plasma. Experimental research is required to quantify the values of these design parameters. Based upon fundamental theory of the transport processes in plasma, some theoretical guidance on the choice of these parameters are provided to help designing the necessary experiments to acquire these data.

Thio, Y. C. Francis↗