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At least 217 records · Page 12

Full-wave modeling of RF waves in fusion plasmas with finite element method: Progress in past decades and its future role

This paper reviews the progress in computing radio frequency (RF) wave fields in fusion plasmas, specifically focusing on simulations utilizing the finite element method (FEM) over the past few decades. Computing RF wave fields in fusion plasmas presents unique challenges due to large simulation domains, complex antenna structures, non-local dielectric properties, and wide ranges of spatial scales. It highlights key developments and outlines future directions, primarily addressing waves in the ion cyclotron (IC) to lower hybrid (LH) frequency range. We begin with briefly revisiting earlier developments before the widespread availability of modern computer-aided engineering (CAE) software based on FEM. This historical perspective illuminates early progress and the physics difficulties that motivated ongoing work within the community. Modern wave simulations for RF antennas based on FEM are characterized by the use of detailed 3D antenna model geometry generated from engineering CAD software and localized wave dielectric model. Significant advancements have also been made in improving physics models to include phenomena such as RF sheath rectification and wave scattering. FEM-based RF simulations have also been applied to compute wave propagation in the core region, where the inclusion of non-local dielectric response is crucial. This is a challenging goal, and several promising approaches have been proposed in this area. Additionally, RF simulation development initiatives based on open-source libraries have gained popularity, demonstrating scalability and flexibility in extending physics models. This paper will discuss the advantages and disadvantages of using such a publicly available FEM library.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Emergent actin flows explain distinct modes of gliding motility

During host infection, Toxoplasma gondii and related unicellular parasites move using gliding, which differs fundamentally from other known mechanisms of eukaryotic cell motility. Gliding is thought to be powered by a thin layer of flowing filamentous (F)-actin sandwiched between the plasma membrane and a myosin-covered inner membrane complex. How this surface actin layer drives the various gliding modes observed in experiments—helical, circular, twirling and patch, pendulum or rolling—is unclear. Here we suggest that F-actin flows arise through self-organization and develop a continuum model of emergent F-actin flow within the confines provided by Toxoplasma geometry. In the presence of F-actin turnover, our model predicts the emergence of a steady-state mode in which actin transport is largely directed rearward. Removing F-actin turnover leads to actin patches that recirculate up and down the cell, which we observe experimentally for drug-stabilized actin bundles in live Toxoplasma gondii parasites. These distinct self-organized actin states can account for observed gliding modes, illustrating how different forms of gliding motility can emerge as an intrinsic consequence of the self-organizing properties of F-actin flow in a confined geometry.

59 BASIC BIOLOGICAL SCIENCES↗

On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability

The magnetic-Rayleigh–Taylor (MRT) instability is a ubiquitous phenomenon that occurs in magnetically-driven Z-pinch implosions. It is important to understand this instability since it can decrease the performance of such implosions. In this work, I present a theoretical model for the weakly nonlinear MRT instability. I obtain such a model by asymptotically expanding an action principle, whose Lagrangian leads to the fully nonlinear MRT equations. After introducing a suitable choice of coordinates, I show that the theory can be cast as a Hamiltonian system, whose Hamiltonian is calculated up to the sixth order in a perturbation parameter. The resulting theory captures the harmonic generation of MRT modes. It is shown that the amplitude at which the linear magnetic-Rayleigh–Taylor instability exponential growth saturates depends on the stabilization effect of the magnetic-field tension. Overall, the theory provides an intuitive interpretation of the weakly nonlinear MRT instability and provides a systematic approach for studying this instability in more complex settings.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamics of hot QCD matter 2024 — Bulk properties

The second Hot QCD Matter 2024 conference at IIT Mandi focused on various ongoing topics in high-energy heavy-ion collisions, encompassing theoretical and experimental perspectives. This proceedings volume includes 19 contributions that collectively explore diverse aspects of the bulk properties of hot QCD matter. The topics encompass the dynamics of electromagnetic fields, transport properties, hadronic matter, spin hydrodynamics, and the role of conserved charges in high-energy environments. These studies significantly enhance our understanding of the complex dynamics of hot QCD matter, the quark–gluon plasma (QGP) formed in high-energy nuclear collisions. Advances in theoretical frameworks, including hydrodynamics, spin dynamics and fluctuation studies, aim to improve theoretical calculations and refine our knowledge of the thermodynamic properties of strongly interacting matter. Experimental efforts, such as those conducted by the ALICE and STAR collaborations, play a vital role in validating these theoretical predictions and deepening our insight into the QCD phase diagram, collectivity in small systems, and the early-stage behavior of strongly interacting matter. In conclusion, combining theoretical models with experimental observations offers a comprehensive understanding of the extreme conditions encountered in relativistic heavy-ion and proton-proton collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Non-Thermal Plasma as a Novel Strategy for Treating or Preventing Viral Infection and Associated Disease

Pathogenic viruses cause many human, animal, and plant diseases that are associated with substantial morbidity, mortality and socio-economic impact. Although effective strategies for combatting virus transmission and associated disease are available, global outbreaks of viral pathogens such as the virus responsible for the COVID-19 pandemic demonstrate that there is still a critical need for new approaches that can be used to interrupt the chain of viral infection and mitigate virus-associated pathogenesis. Recent studies point to non-thermal plasma (NTP), a partly ionized gas comprised of a complex mixture of reactive oxygen and nitrogen species along with physical effectors, as the potential foundation for new antiviral approaches. A more thorough understanding of the antiviral properties and safety of NTP has stimulated explorations of NTP as the basis for treatments of viral diseases. The recently described immunomodulatory properties of NTP are also being evaluated for potential use in immunotherapies of viral diseases as well as in antiviral vaccination strategies. In this review, we present the current state-of-the-art in addition to compelling arguments that NTP merits further exploration for use in the prevention and management of viral infections and associated diseases.

60 APPLIED LIFE SCIENCES↗

Finite ion temperature effects on electrostatic instabilities in partially magnetized plasmas

In this paper, the effects of warm ions on electrostatic, kinetic instabilities observed in partially magnetized plasmas, such as the electron cyclotron drift instability (ECDI) and modified two-stream instability (MTSI), are investigated. The kinetic dispersion relation that accounts for warm, non-magnetized ions and warm, magnetized electrons is solved using a complex root-finding technique [A. C. Denig and K. Hara, Phys. Plasmas 30, 032108 (2023)]. It is observed that finite ion temperature introduces ion Landau damping effects, decreasing the growth rate of most unstable modes. The high-frequency, short-wavelength ECDI modes are more strongly affected by ion Landau damping than the low-frequency, long-wavelength MTSI modes. The solutions of the kinetic dispersion relation for MTSI are compared with the fluid dispersion relation of MTSI, which was originally proposed by McBride et al. [Phys. Fluids 15 2367–2383 (1972)]. The differences in the dispersion characteristics between the kinetic and fluid MTSI limits are assessed, illustrating the effects of electron and ion Landau damping on kinetic instabilities in partially magnetized plasmas.

Denig, A. C. (ORCID:0000000253339572)↗

Adaptive Critical Balance and Firehose Instability in an Expanding, Turbulent, Collisionless Plasma

Abstract Using a hybrid-kinetic particle-in-cell simulation, we study the evolution of an expanding, collisionless, magnetized plasma in which strong Alfvénic turbulence is persistently driven. Temperature anisotropy generated adiabatically by the plasma expansion (and consequent decrease in the mean magnetic-field strength) gradually reduces the effective elasticity of the field lines, causing reductions in the linear frequency and residual energy of the Alfvénic fluctuations. In response, these fluctuations modify their interactions and spatial anisotropy to maintain a scale-by-scale “critical balance” between their characteristic linear and nonlinear frequencies. Eventually the plasma becomes unstable to kinetic firehose instabilities, which excite rapidly growing magnetic fluctuations at ion-Larmor scales. The consequent pitch-angle scattering of particles maintains the temperature anisotropy near marginal stability, even as the turbulent plasma continues to expand. The resulting evolution of parallel and perpendicular temperatures does not satisfy double-adiabatic conservation laws, but is described accurately by a simple model that includes anomalous scattering. Our results have implications for understanding the complex interplay between macro- and microscale physics in various hot, dilute, astrophysical plasmas, and offer predictions concerning power spectra, residual energy, ion-Larmor-scale spectral breaks, and non-Maxwellian features in ion distribution functions that may be tested by measurements taken in high-beta regions of the solar wind.

79 ASTRONOMY AND ASTROPHYSICS↗

Charging and ion ejection dynamics of large helium nanodroplets exposed to intense femtosecond soft xray pulses

Ion ejection from charged helium nanodroplets exposed to intense femtosecond soft X-ray pulses is studied by single-pulse ion time-of-flight (TOF) spectroscopy in coincidence with small-angle X-ray scattering. Scattering images encode the droplet size and absolute photon flux incident on each droplet, while ion TOF spectra are used to determine the maximum ion kinetic energy, Ekin, of He+ j fragments (j = 1-4). Measurements span HeN droplet sizes between N similar to 10(7) and similar to 10(10) (radii R-0 = 78-578 nm), and droplet charges between similar to 9x10(-5) and similar to 3x10(-3) e/atom. Conditions encompass a wide range of ionization and expansion regimes, from departure of all photoelectrons from the droplet, leading to pure Coulomb explosion, to substantial electron trapping by the electrostatic potential of the charged droplet, indicating the onset of hydrodynamic expansion. The unique combination of absolute Xray intensities, droplet sizes, and ion Ekin on an event-by-event basis reveals a detailed picture of the correlations between the ionization conditions and the ejection dynamics of the ionic fragments. The maximum E-kin of He+ is found to be governed by Coulomb repulsion from unscreened cations across all expansion regimes. The impact of ion-atom interactions resulting from the relatively low charge densities is increasingly relevant with less electron trapping. The findings are consistent with the emergence of a charged spherical shell around a quasineutral plasma core as the degree of ionization increases. The results demonstrate a complex relationship between measured ion E-kin and droplet ionization conditions that can only be disentangled through the use of coincident single-pulse TOF and scattering data.

Helium↗

Plasma-based global pathway analysis to understand the chemical kinetics of plasma-assisted combustion and fuel reforming

The Global Pathway Analysis (GPA) algorithm helps analyze the chemical kinetics of complex combustion systems by identifying important global reaction pathways connecting a source species to a sink species through various important intermediate species (i.e., hub species). Here, the present work aims to extend GPA algorithm to plasma-assisted combustion and fuel reforming systems to identify the dominant global pathways in such systems at various conditions. In addition, the present study extends the ability of GPA algorithm to identify reaction cycles involving the excitation of high-concentration species (e.g., O 2 , N 2 , and fuel) to their vibrational and electronic states and the subsequent de excitation to their ground state, based on their significance on the reactivity of plasma-assisted systems in terms of gas heating and radical production. Provisions are made in the GPA algorithm to evaluate the reactivity of identified re action pathways and cycles based on the element-flux transfer (i.e., dominance), heat release, and radical production rate. The newly developed Plasma-based Global Pathway Analysis (PGPA) algorithm is then used to analyze the plasma assisted combustion of ammonia and reforming of methane. The PGPA analyses elucidated the significance of vibrational-translational cycles on the reactivity of NH 3 /air mixtures. Further, analyses on the production of NO ascribed the early reforming of NH 3 to N 2 and H 2 in impeding the production of NO during plasma-assisted NH 3 ignition. Lastly, the enhanced reforming of CH 4 /N 2 mixtures using plasma has been attributed to electron impact dissociation of CH 4 when compared to thermal reforming. In contrast, conventional path-Flux analysis (PFA) was found to require significant manual effort and pre-analysis intuitions from expert knowledge, making it arduous to provide valuable in sights into plasma chemistry. The user-friendly and automated nature of PGPA thus provides a valuable tool for assessing the kinetics of plasma-assisted systems helpful in analyzing and, further, a foundation in reducing plasma-assisted chemistry, without the needs of expert knowledge.

33 ADVANCED PROPULSION SYSTEMS↗

Spectroscopic signatures and oxidation characteristics of nanosecond laser-induced cerium plasmas

Improving technologies related to the wide area environmental sampling of nuclear materials supports the nuclear nonproliferation mission of preventing the proliferation of nuclear weapons by monitoring nuclear weapons tests and detecting undeclared nuclear fuel cycle activities. Standoff, laser-based detection techniques such as laser-induced breakdown spectroscopy have the potential to offer robust, field-deployable methods that provide rapid element-specific and phase identifiable measurements over a wide range of materials. This work aims to elucidate the effects of atmospheric conditions and oxidation reactions on the highly complex and transient spectroscopic signatures of laser-induced plutonium surrogate plasmas. Time-resolved spectra of nanosecond laser ablation cerium plasmas were measured using laser-induced breakdown spectroscopy in a range of atmospheres containing low to high concentrations of oxygen. Here, the growth of strong CeO molecular emission bands was observed in the visible spectrum, where it was shown that the persistence of CeO is reduced from around 60 μs to 50 μs in oxygen rich atmospheric environments. To further investigate the growth and depletion of CeO in the laser-produced plasma, ratios of CeO-to-Ce emission were generated using integrated intensities corresponding to the Q-branch of the CeO D 1 -X 1 transitions and numerous strong atomic Ce peaks. It was determined that the fastest rate of formation of CeO in argon occurred for moderate oxygen mass fractions between 0.10 and 0.15 while the ratios were reduced at higher oxygen mass fractions (i.e., Y O 2 = 0.20) due to competing oxidation reactions and lower plasma temperatures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Reaction mechanism for atmospheric pressure plasma treatment of cysteine in solution

Mechanisms for the cold atmospheric plasma (CAP) treatment of cells in solution are needed for more optimum design of plasma devices for wound healing, cancer treatment, and bacterial inactivation. However, the complexity of organic molecules on cell membranes makes understanding mechanisms that result in modifications (i.e. oxidation) of such compounds difficult. As a surrogate to these systems, a reaction mechanism for the oxidation of cysteine in CAP activated water was developed and implemented in a 0-dimensional (plug-flow) global plasma chemistry model with the capability of addressing plasma-liquid interactions. Reaction rate coefficients for organic reactions in water were estimated based on available data in the literature or by analogy to gas-phase reactions. The mechanism was validated by comparison to experimental mass-spectrometry data for COST-jets sustained in He/O 2 , He/H 2 O and He/N 2 /O 2 mixtures treating cysteine in water. Results from the model were used to determine the consequences of changing COST-jet operating parameters, such as distance from the substrate and inlet gas composition, on cysteine oxidation product formation. Results indicate that operating parameters can be adjusted to select for desired cysteine oxidation products, including nitrosylated products.

60 APPLIED LIFE SCIENCES↗

Insights into Sustainable Nitrogen Fixation by Gas-phase Spectroscopic Measurements and Global Modeling of Reaction Intermediates in Humid Nitrogen Plasma

In this article, there is growing interest in reacting molecular nitrogen and water to sustainably synthesize fixed forms of nitrogen such as ammonia. In particular, low-temperature plasmas can activate these relatively inert feedstocks at or near room temperature without a catalyst. However, because of the enhanced reactivity and nonequilibrium chemistry, a diverse range of products is formed, and the underlying reaction mechanisms are exceedingly complex. In this work, we studied a simplified reactor consisting of a gaseous plasma containing controlled mixtures of nitrogen gas and water vapor. Densities of key chemical species such as N, H, OH, NH, and NO were measured by emission and laser-based spectroscopy as a function of the relative humidity. A global model was constructed and the reaction network was validated by comparing calculated species densities with experiments. We discover that N, a key initial intermediate for ammonia, strongly decreases in the presence of water vapor, and as a result, ammonia formation becomes limited at high relative humidity. This decrease is surprisingly not because N itself reacts, but because one of its main sources, an excited molecular nitrogen state, is reacted away. In addition, oxidation pathways for nitrogen, which lead to NO and related products, are found to be favored over reduction pathways because the corresponding reverse reactions are less significant. Together, this understanding helps explain previously reported observations of selectivity toward nitrogen oxides over ammonia, particularly at higher relative humidities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measurement of atomic oxygen densities using TALIF on a dielectric barrier discharge: insights into the volume above a micro cavity plasma array

Dielectric barrier discharges, particularly micro cavity plasma arrays, offer significant potential for plasma-catalytic research due to their ability to ignite plasma in direct contact with a catalytic surface, enabling the observation of plasma-surface interactions. A key factor in their application is the generation of reactive species, such as atomic oxygen, within the cavities. These species can interact with both the surface (e.g. for activation or cleaning) and the gas being treated (e.g. for oxidation). Given the central role of oxygen atoms in plasma catalysis and their use as a model for more complex species, this work investigates the transport of these atoms out of the cavities. Two-photon absorption laser-induced fluorescence spectroscopy with picosecond laser excitation is performed in the volume above the cavities. The results are compared with a basic diffusion model. The reactor operates with a He/O 2 mixture at a flow rate of 1 slm and atmospheric pressure. Densities of up to 10 16 cm -3 are measured near the surface. Time-dependent measurements show that, at a distance of 350 µm from the surface, a density equilibrium is reached within less than 3 ms of reactor operation. Decay times due to ozone formation after the reactor is turned off are on a similar scale. Spatially resolved measurements show that the oxygen density decreases exponentially from the surface but remains detectable up to approximately 1 mm above the surface, indicating significant application potential. Variations in the O 2 admixture show a density maximum at 0.4%, confirming previous helium state enhanced actinometry measurements within the cavities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

In situ Detection of Plasma Induced Surface Interaction based on Deep Learning based Visual Diagnostics (Technical Report)

It is characteristic for many plasma devices to undergo plasma-material interaction leading to surface erosion. These processes, often not easily detectable, lead to changes in device performance and lifespan. State-of-the-art lifetime tests and wear experiments require over 1000s hours. A self-consistent model for accurately predicting the erosion's effects is not available. In situ detection of these processes is not a trivial task since the surface variations at the early stages have a micron scale. Such limitations not only restrict testing and prediction capabilities but also slow the development of new thrusters and limit mission duration. To address these challenges, an in-situ diagnostic for real-time erosion assessment has been developed, aiming to expedite lifetime testing and broaden experimental campaigns. Several works were dedicated to real-time and in situ monitoring of material erosion during plasma exposure using laser holography, microscopy, and with telemicroscopes. However, the applicability of these approaches is limited due to complexity, cost and less flexibility as they often require placing diagnostic equipment inside the vacuum chamber. In collaboration with Princeton Collaborative Research Facility (PCRF), Princeton Plasma Physics Laboratory (PPPL), a new diagnostic approach is developed, where geometry modifications to the ceramic channel walls were introduced that would result in accelerated channel erosion. We employed Long-distance microscope (LDM) imagery, combined with Deep-Learning based Shape from focus or depth from focus (DFF or SFF) approach, that provides an accessible and cost-effective solution. LDM employs focus variation techniques to continuously capture multiple images of the target object at distinct focal planes. DFF, an optical focus variation method, generates a 3D topographical surface depth map from a sequence of variably focused images. Combined with the developed diagnostic, this approach offers a controllable means to study erosion under accelerated conditions. In this work, we develop Neural Network-based DFF algorithm applicable for LDM data to quantitatively evaluate plasma induced surface modification from LDM data. Next, we develop Deep Learning-based super-resolution depth map image reconstruction technique to increase the resolution of depth maps obtained from DFF algorithm to improve the accuracy of erosion measurements. Thirdly, we develop several image processing techniques to remove noise and improve the quality of depth map image. Here we report the results of initial tests for this approach. An experimental setup designed and built in PPPL was employed that consists of a 3-cm gridded ion source that produces a neutralized argon beam with energies up to 600 eV. A hexagonal boron nitride (h-BN) ceramic target, designed based on computational predictions, was used. Tests were conducted to reconstruct the complex geometry of the target under the lighting conditions of the operated ion source.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dispersion relation and instability for an anisotropic nonuniform flowing plasma

A generalized formula for wave instability is developed for an anisotropic nonuniform plasma with finite flows and temperatures. Six-moment fluid equations are solved to give the analytic expression for wave instability in arbitrarily nonuniform plasmas. The analytic formula explicitly states the dependence of wave instability on the nonuniformities of number density, flow velocity, and anisotropic or isotropic pressure. The accuracy of the formalism is verified by a numerical calculation of implicit dispersion relations in complex Fourier space. The analysis shows that nonuniformity plays a critical role in plasma instability, while the flow velocity and anisotropic pressures determine the growth rate of the instability. Lastly, the instability diagram and associated instability criterion for anisotropy-driven instability are introduced as applications of the formalism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Three-wave coupling observed between a shear Alfvén wave and a kink-unstable magnetic flux rope

Results from a laboratory experiment are presented in which, for the first time, a shear Alfvén wave is launched using an antenna in a current-carrying plasma column that is tailored to be either stable or unstable to the kink oscillation. As the plasma is driven kink unstable, the frequency power spectrum of the Alfvén wave evolves from a single peak to a peak with multiple sidebands separated by integer multiples of the kink frequency. The main sidebands (one on either side of the launched wave peak in the power spectrum) are analyzed using azimuthal wavenumber matching, perpendicular and parallel wavenumber decomposition, and bispectral time series analysis. The dispersion relation and three-wave matching conditions are satisfied, given each sideband is a propagating Alfvén wave that results from the interaction of the pump Alfvén wave and the co-propagating component of a half-wavelength, standing kink mode. The interaction is shown to generate smaller perpendicular wavelength Alfvén waves that drive energy transport to scales that will approach the dissipation scale of k⊥ρs=1, with k⊥ being the perpendicular wavenumber and ρs being the ion gyroradius at the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An alternate route for cellulose microfibril biosynthesis in plants

Similar to cellulose synthases (CESAs), cellulose synthase–like D (CSLD) proteins synthesize β-1,4-glucan in plants. CSLDs are important for tip growth and cytokinesis, but it was unknown whether they form membrane complexes in vivo or produce microfibrillar cellulose. We produced viable CESA-deficient mutants of the moss Physcomitrium patens to investigate CSLD function without interfering CESA activity. Microscopy and spectroscopy showed that CESA-deficient mutants synthesize cellulose microfibrils that are indistinguishable from those in vascular plants. Correspondingly, freeze-fracture electron microscopy revealed rosette-shaped particle assemblies in the plasma membrane that are indistinguishable from CESA-containing rosette cellulose synthesis complexes (CSCs). Our data show that proteins other than CESAs, most likely CSLDs, produce cellulose microfibrils in P. patens protonemal filaments. The data suggest that the specialized roles of CSLDs in cytokinesis and tip growth are based on differential expression and different interactions with microtubules and possibly Ca 2+ , rather than structural differences in the microfibrils they produce.

59 BASIC BIOLOGICAL SCIENCES↗

Generative Physics-Informed Neural Network Solving Multi-Scale and Multi-Phase Plasma Chemical Flow Field

Low-temperature plasmas (LTPs) are non-equilibrium systems with near-room-temperature gas and highly energetic electrons. This makes them ideal for delicate applications in biomedicine and semiconductor manufacturing, enabling processes like wound healing, sterilization, etching, and plasma-enhanced chemical vapor deposition without thermal damage. However, LTPs involve complex chemistries, with hundreds of species and thousands of reactions, complicating their diagnosis, prediction, and control. Conventional diagnostics, such as Fourier-transform infrared spectroscopy (FTIR), laser-induced fluorescence (LIF), and optical emission spectroscopy (OES), offer limited species detection, while mass spectrometry (MS) struggles with low-sensitivity species. Additionally, LTP simulations face multi-scale challenges, as macroscopic fluid dynamics and microscopic particle collisions operate on vastly different timescales. To address these issues, we developed an artificial intelligence (AI) based diagnostic system: a generative physics-informed neural network (PINN-Gen) that can predict spatially resolved species concentrations and temperatures in LTPs by integrating experimental data from planar LIF with microscopic plasma chemical kinetics and macroscopic fluid mechanics, including plasma-liquid interactions at the interface between two phases. PINN-Gen solves no equations but checks the errors of physical laws by substituting the output from neural network, and the comparison with the experimental results. Thus, it naturally avoids the multi-scale difficulty of numerical simulations and predicts the results of conventionally unsolvable multi-scale and multi-phase problems. The real-time prediction will be robust due to the physical information used in the training of such a neural network, and only very limited input of condition required due to its generative feature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗