Search NASA⌕ Search

SEARCH · Search NASA

Results for “Strong coupling constant”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗
DOE OSTI2021

Collective Phonon–Polaritonic Modes in Silicon Carbide Subarrays

Localized surface phonon polaritons (LSPhPs) can be implemented to engineer light–matter interactions through nanoscale patterning for a range of midinfrared application spaces. However, the polar material systems studied to date have mainly focused on simple designs featuring a single element in the periodic unit cell. Increasing the complexity of the unit cell can serve to modify the resonant near-fields and intra- and inter-unit-cell coupling as well as to dictate spectral tuning in the far-field. In this work, we exploit more complicated unit-cell structures to realize LSPhP modes with additional degrees of design freedom, which are largely unexplored. Collectively excited LSPhP modes with distinctly symmetric and antisymmetric near-fields are supported in these subarray designs, which are based on nanopillars that are scaled by the number of subarray elements to ensure a constant unit-cell size. Moreover, we observe an anomalous mode-matching of the collective symmetric mode in our fabricated subarrays that is robust to changing numbers of pillars within the subarrays as well as to defects intentionally introduced in the form of missing pillars. This work therefore illustrates the hierarchical design of tailored LSPhP resonances and modal near-field profiles simultaneously for a variety of IR applications such as surface-enhanced spectroscopies and biochemical sensing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Laser pulse-length dependent ablation and shock generation in silicon at 5 × 10 14 W/ cm 2 intensities

The effect of laser pulse duration on energy coupling into a planar silicon target is investigated in experiments at the OMEGA-EP facility by varying the laser pulse length τ —spanning 3 orders of magnitude from 100 ps to 10 ns—while maintaining a constant peak laser intensity, I 0 = 5 × 10 14 W/ cm 2 . In theoretical models, the ablation pressure primarily scales for a given material with laser intensity and wavelength, which are all fixed variables here, allowing us to explore the specific role of laser pulse duration. Two-dimensional radiation-hydrodynamics simulations benchmarked with optical probing of the expanding plasma show that the pulse duration is critical for the ablation pressure to reach a steady state. Moreover, the pulse duration impacts shock decay and multiple wave effects, which strongly dictate the evolving shock profile that propagates within the laser-shocked target as ultimately measured by rear-surface diagnostics. The shock velocities inferred from the theoretical model, after considering shock decay, impedance matching, and shock Hugoniot, are found to be in good agreement with velocimetry measurements. However, discrepancies are observed with simulations for the shorter (0.1 ns) and longer (10 ns) pulse durations, which are respectively attributed to unaccounted contributions of kinetic absorption mechanisms and instabilities in simulations. Published by the American Physical Society 2024

Bailly-Grandvaux, M. (ORCID:0000000175294013)↗
DOE OSTI2022

Formation and detection of metastable formic acid in a supersonic expansion: High resolution infrared spectroscopy of the jet-cooled cis -HCOOH conformer

High-resolution direct absorption infrared spectra of metastable cis-formic acid (HCOOH) trapped in a cis-well resonance behind a 15 kcal/mol barrier are reported for the first time, with the energetically unstable conformer produced in a supersonic slit plasma expansion of trans-formic acid/H 2 mixtures. We present a detailed high-resolution rovibrational analysis for cis-formic acid species in the OH stretch (ν 1 ) fundamental, providing first precision vibrational band origin, rotational constants, and term values, which in conjunction with ab initio calculations at the couple-cluster with single, double, and perturbative triple [CCSD(T)]/ANOn (n = 0, 1, 2) level support the experimental assignments and establish critical points on the potential energy surface for internal rotor trans-to-cis isomerization. Relative intensities for a- and b-type transitions observed in the spectra permit the transition dipole moment components to be determined in the body fixed frame and prove to be in good agreement with ab initio CCSD(T) theoretical estimates but in poor agreement with simple bond-dipole predictions. As a result, the observed signal dependence on H 2 in the discharge suggests the presence of a novel H atom radical chemical mechanism for strongly endothermic “up-hill” internal rotor isomerization between trans- and cis-formic acid conformers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1983

Ion trajectories in a space-charge wave on a relativistic electron beam

The motion of an ion in a space-charge wave on a strongly magnetized electron beam is investigated. The motions of the ion perpendicular and parallel to the beam direction are coupled by a nonlinear term in the ion Hamiltonian that is proportional to the wave amplitude, and this coupling causes the motion of the ion to deviate significantly from that of a linear harmonic oscillator in certain resonant regions of phase space. A sequence of canonical transformations is employed to investigate the motion of the ion in these regions. It is determined that wave amplitudes that are too small to trap beam electrons are too small to cause these resonances to overlap. When this overlap does not occur, the motion is found not to be discernibly ergodic in any three-dimensional subspace of the energy hypersurface because there exists a third constant of the motion in addition to the total energy and angular momentum. The numerically integrated ion trajectories are studied using surface-of-section techniques in order to verify these findings. It is found that the third constant of the motion constrains an ion initially trapped in a potential well of the wave to remain trapped in this well. It is concluded that ergodic behavior poses no threat at attempts at collective ion acceleration in space-charge waves on an electron beam.

Russell, D. A.↗
DOE OSTI2026

Influence of plateau, slope, and valley on soil hydrology during the dry season in a Central Amazon old‐growth forest

Soil moisture regulates plant water supply and drought sensitivity in tropical forests, yet its vertical and topographic variation remains poorly characterized. We combined high-frequency time-domain reflectometry measurements from 5 to 100 cm across plateau, slope, and valley landforms at the Zona Florestal 2 research site north of Manaus, Central Amazonia, to quantify how soil moisture memory, timing of responses to rainfall, dry-down rates (τ), and soil–water depletion vary across these contrasting landforms. Landform-specific soil moisture calibration curves ensured accurate volumetric water content estimates in these highly weathered soils. During the 2023 dry-to-wet transition (August–November), soil moisture memory showed strong topographic contrasts, with valley profiles increasing from ∼47 h at 5 cm to ∼154 h at 100 cm, while plateaus exhibited higher near-surface persistence (∼124 h at 5 cm) but weaker memory at depth. Dry-down behavior reinforced these differences as valley soils exhibited τ values exceeding ∼200 h, more than double the characteristic τ of plateau soils (∼90 h). Rainfall–soil moisture correlations indicated immediate responses at shallow depths in valleys and progressively longer lags with depth on plateaus and slopes. These hydrologic patterns were mirrored in depletion profiles, which declined sharply below 30 cm on plateaus but remained high and sustained throughout the upper meter in slopes and valleys. Together, these findings provide the first depth-resolved field measurements of soil moisture memory, rainfall coupling, dry-down constants, and depletion dynamics across major upland landforms in Central Amazonia and offer clear observational benchmarks for improving land-surface and ecosystem model representations of soil–water processes.

Hillslope↗
DOE OSTI2021

High-Entropy Ceramic Coatings: Transformative New Materials for Environmentally-Compatible Thin-Film Insulators against High-T Molten Salts

An emerging new class of promising materials, High-Entropy Ceramics (HECs) or Compositionally-Complex Ceramics (CCCs), have been successfully fabricated in the last three years. This project evaluates HECs/CCCs in the concentrated solar power (CSP) context. In this project, we have identified a couple of simple, and key descriptors governing thermal conductivity in HECs. Size disorder among the cations was found to have a strong influence on the thermal conductivity across multiple systems and throughout a vast compositional space. Since identifying this, we have optimized previous compositions to achieve low thermal conductivities of $k$~$1-1.4Wm{-1}K{-1}$. We have further reduced our selection of promising compositions based on project guidelines and applied a theory that can potentially predict reactivity with molten salts to identify a small set of HECs that are suitable for further molten salt heat transfer media (HTM) stability testing. Many compositions reveal poor resistance to molten chloride salt after being exposed for 24 h compared to the reference structural alloy, Haynes 230. However, after 100 h, a few HECs/CCCs show strong parabolic rate constant effects and provide greater resistance to chloride salt compared to Haynes 230 alloy, which shows more linear kinetics. Postmortem characterization of the microstructure reveals the parabolic rate constant originates from a dense reaction layer form at the interface. This feature is absent in Haynes 230, which only shows grain boundary infiltration. The HECs/CCCs were also put in contact with the metal alloy under Ar for 800 h at 800°C and show negligible interaction. Lastly, parabolic rate constant HECs/CCCs also have low thermal conductivity $(<2 Wm^{-1} K^{-1})$ at 800°C. These specimens satisfy all project requirements and demonstrate their promising application in next-generation CSP.

14 SOLAR ENERGY↗
NASA NTRS1993

New technologies for UV detectors

Several technologies are currently being developed, leading to substantial improvements in the performance of UV detectors or significant reductions in power or weight. Four technologies discussed are (1) thin-film coatings to enhance the UV sensitivity of CCD's, (2) highly innovative magnet assemblies that dramatically reduce weight and result in virtually no external flux, (3) new techniques for curving microchannel plates (MCP's) so that single plates can be used to prevent ion feedback and present highly localized charge clouds to an anode structure, and (4) high-performance alternatives to glass-based MCP's. In item (2), for example, very robust magnets are made out of rare earth materials such as samarium cobalt, and cladding magnets are employed to prevent flux from escaping from the detector into the external environment. These new ultralight magnet assemblies are able to create strong, exceptionally uniform magnetic fields for image intensification and focusing of photoelectrons. The principle advantage of such detectors is the quantum efficiencies of 70-80 percent obtained throughout ultraviolet wavelengths (900-2000 A), the highest of any device. Despite the improvements achieved under item (3), high-performance alternatives to conventional glass-based MCP's potentially offer three distinct new advantages that include (1) a 30-100-fold improvement in dynamic range resulting in correspondingly higher signal-to-noise ratios, (2) the use of pure dielectric and semiconductor materials that will not outgas contaminants that eventually destroy photocathodes, and (3) channels that have constant spacing providing long-ranged order since the plates are made using photolithography techniques from the semiconductor industry. The manufacturers of these advanced-technology MCP's, however, are a couple of years away from actually producing a functioning image intensifier. In contrast to the use of CCD's for optical, ground based observations, there is no single detector technology in the ultraviolet that dominates or is as universally suitable for all applications. Thus, several technological problems, recent advances, and the impact that these new enabling technologies represent for UV applications are addressed.

Joseph, C. L.↗
DOE OSTI2021

Strong influence of nonmagnetic ligands on the momentum-dependent spin splitting in antiferromagnets

Here, recent studies show the nonrelativistic antiferromagnetic ordering could generate momentum-dependent spin splitting analogous to the Rashba effect but free from the requirement of relativistic spin-orbit coupling. Whereas the classification of such compounds can be illustrated by different spin-splitting prototypes (SSTs) from symmetry analysis and density-functional-theory calculations, the huge variation in chemical bonding and structures of these diverse compounds possibly clouds the issue of how much of the variation in spin splitting can be traced back to the symmetry-defined characteristics, rather to the underlining chemical and structural diversity. The alternative model Hamiltonian approaches do not confront the issues of chemical and structural complexity but often consider only the magnetic sublattice, dealing with the all-important effects of the nonmagnetic ligands via renormalizing the interactions between the magnetic sites. To this end, we constructed a DFT model Hamiltonian that allows us to study SSTs at constant chemistry while retaining the realistic atomic-scale structure including ligands. This is accomplished by using a single, universal magnetic skeletal lattice (Ni 2+ ions in rocksalt NiO) and designing small displacements of the nonmagnetic (oxygen) sublattice which produce, by design, the different SST magnetic symmetries. We show that (i) even similar crystal structures having very similar band structures can lead to contrasting behavior of spin splitting vs momentum, and (ii) even subtle deformations of the nonmagnetic ligand sublattice could cause a giant spin splitting in AFM-induced SST. This is a paradigm shift relative to the convention of modeling magnets without considering the nonmagnetic ligand that mediates indirect magnetic interaction (e.g., superexchange).

36 MATERIALS SCIENCE↗
NASA NTRS1991

Nonlinear development and secondary instability of Gortler vortices in hypersonic flows

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Goertler vortices is the temperature adjustment layer over which the basic state temperature decreases monotonically to its free stream value. Except for a special wall curvature distribution, the evolution of Goertler vortices trapped in the temperature adjustment layer will in general be strongly affected by the boundary layer growth through the O(M sup 3/2) curvature of the basic state, where M is the free stream Mach number. Only when the local wavenumber becomes as large as of order M sup 3/8, do nonparallel effects become negligible in the determination of stability properties. In the latter case, Goertler vortices will be trapped in a thin layer of O(epsilon sup 1/2) thickness which is embedded in the temperature adjustment layer; here epsilon is the inverse of the local wavenumber. A weakly nonlinear theory is presented in which the initial nonlinear development of Goertler vortices in the neighborhood of the neutral position is studied and two coupled evolution equations are derived. From these, it can be determined whether the vortices are decaying or growing depending on the sign of a constant which is related to wall curvature and the basic state temperature.

Fu, Yibin B.↗
NASA NTRS1989

Nonlinear interactions in mixing layers and compressible heated round jets

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Jarrah, Yousef Mohd↗
NASA NTRSDate not supplied

Cloud Condensation Nuclei in the Early Martian Atmosphere

Explanations for how early Mars supported warmer and wetter conditions 3.5 to 4 billion years ago have long been debated. A water cloud greenhouse has been proposed as a mechanism of warming early Mars, but modeling studies of these environments produce mixed results. Studies show that both H 2 O and CO 2 clouds are capable of influencing atmospheric and surface temperatures, but the amount of warming induced is very sensitive to the cloud physics assumptions made. Producing a strong water cloud greenhouse effect is dependent on forming clouds as high in the atmosphere as possible to maximize warming. However, the majority of studies of H 2 O and CO 2 clouds on early Mars assume that a constant number of seed nuclei are available at all altitudes for clouds to condense onto. Here we test the validity of this assumption in massive CO 2 atmospheres. Explaining how dust is lofted into the middle atmosphere to serve as seed nuclei for cloud formation is a challenge even for present day Mars. This problem may change in an early Mars environment where having a more massive atmosphere could result in differences in the general circulation, vertical transport, and settling time scales of dust. Here, we begin a first-ever study of the early Mars dust cycle and how it might couple to the water cycle. We present early Mars simulations in which dust is injected at the surface and can be transported throughout the atmosphere. We explore the resulting vertical and horizontal distributions of dust particles and their sizes with an emphasis on the maximum height of the dust. We aim to investigate what the distribution of cloud condensation nuclei may have been on early Mars and how this might impact cloud formation.

Kathryn Steakley↗
DOE OSTI2023

Dynamical effects from anomalies: Modified electrodynamics in Weyl semimetals

Here, we discuss the modified quantum electrodynamics from a time-reversal-breaking Weyl semimetal coupled with a U⁡(1) gauge (electromagnetic) field. A key role is played by the soft dispersion of the photons in a particular direction, say $\hat{z}$, due to the Hall conductivity of the Weyl semimetal. Due to the soft photon, the fermion velocity in $\hat{z}$ is logarithmically reduced under renormalization group flow, together with the fine-structure constant. Meanwhile, fermions acquire a finite lifetime from spontaneous emission of the soft photon, namely, the Cherenkov radiation. At low-energy E, the inverse of the fermion lifetime scales as τ -1 ~E/PolyLog⁡(E). Therefore, even though fermion quasiparticles are eventually well-defined at very low energy, over a wide intermediate energy window the Weyl semimetal behaves like a marginal Fermi liquid. Phenomenologically, our results are more relevant for emergent Weyl semimetals, where the fermions and photons all emerge from strongly correlated lattice systems. Possible experimental implications are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Photoinduced charge transfer in Zn(II) and Au(III)-ligated symmetric and asymmetric bacteriochlorin dyads: A computational study

The excited-state properties and photoinduced charge-transfer (CT) kinetics in a series of symmetrical and asymmetrical Zn- and Au-ligated meso–meso-connected bacteriochlorin (BChl) complexes are studied computationally. BChl derivatives, which are excellent near-IR absorbing chromophores, are found to play a central role in bacterial photosynthetic reaction centers but are rarely used in artificial solar energy harvesting systems. The optical properties of chemically linked BChl complexes can be tuned by varying the linking group and involving different ligated metal ions. We investigate charge transfer in BChl dyads that are either directly linked or through a phenylene ring (1,4- phenylene) and which are ligating Zn or Au ions. The directly linked dyads with a nearly perpendicular arrangement of the BChl units bear markedly different properties than phenylene linked dyads. In addition, we find that the dielectric dependence of the intramolecular CT rate is very strong in neutral Zn-ligated dyads, whereas cationic Au-ligated dyads show negligible dielectric dependence of the CT rate. Rate constants of the photo induced CT process are calculated at the semiclassical Marcus level and are compared to fully quantum mechanical Fermi’s golden rule based values. The rates are calculated using a screened range separated hybrid functional that offers a consistent framework for addressing environment polarization. We study solvated systems in two solvents of a low and a high scalar dielectric constant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Fathoming the anisotropic magnetoelasticity and magnetocaloric effect in GdNi

Intermetallic GdNi adopts a CrB type of crystal structure (space group Cmcm), and it orders ferromagnetically via a second-order phase transition at 70 K, exhibiting unusually strong spontaneous striction along the three independent crystallographic axes in the ferromagnetically ordered state. Here we introduce a microscopic model to describe anisotropic changes of lattice parameters and elastic contribution to magnetocaloric effect of GdNi. In the model, results of density functional theory (DFT) calculations are used as inputs into a Hamiltonian that includes elastic energy of an anisotropic crystal lattice, exchange interactions, and Zeeman effect. The magnetic and elastic Hamiltonians are coupled through an anisotropic Bean-Rodbell model of magnetoelastic interactions. This coupling gives rise to anisotropic changes in the lattice parameters observed experimentally, and the model reveals good to reasonable agreements between the current theoretical results and earlier experimental data, thus validating the model within the limits of assumptions made. We also show that DFT calculations with 4f electrons of Gd treated as core electrons lead to a more adequate estimate of elastic constants of GdNi in comparison with the LDA + U method where 4f electrons are treated as valence electrons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Deconstruction of the Anisotropic Magnetic Interactions from Spin‐Entangled Optical Excitations in van der Waals Antiferromagnets

Magneto-optical excitations in antiferromagnetic d systems can originate from a multiplicity of light-spin and spin-spin interactions, as the light and spin degrees of freedom can be entangled. This is exemplified in van der Waals systems with attendant strong anisotropy between in-plane and out-of-plane directions, such as MnPS 3 and NiPS 3 films studied here. The rich interplay between the magnetic ordering and sub-bandgap optical transitions poses a challenge to resolve the mechanisms driving spin-entangled optical transitions, as well as the single-particle bandgap itself. Here, a high-fidelity ab initio theory is applied to find a realistic estimation of the bandgap by elucidating the atom- and orbital-resolved contributions to the fundamental sub-bands. It is further demonstrated that the spin-entangled excitations, observable as photoluminescence and absorption resonances, originate from an on-site spin-flip transition confined to a magnetic atom (Mn or Ni). The evolution of the spin-flip transition in a magnetic field is used to deduce the effective exchange coupling and anisotropy constants.

2D materials↗
NASA NTRS1973

Repeated cascade theory of homogeneous turbulence.

The problem of turbulent spectrum engenders two coupled hierarchies: one originates from the development of stress, leading to a transfer function, and the other from the development of an eddy viscosity. In order to incorporate physical roles among scales, the turbulent velocity fluctuation is decomposed into a series of ranks in the increasing order of randomness, contributing successively to energy or stress, eddy viscosity, relaxation frequency, and higher-rank frequencies in the memory chain. As a result, the first hierarchy mentioned above becomes closed at the quadrupole correlation. The second hierarchy governs the eddy viscosities of different ranks, related to relaxation frequencies of such ranks, in the form of a memory chain. It is cut off by an implicit viscous mechanism. For zero wind gradient, the spectrum in the inertial subrange recovers the Kolmogoroff k to the minus 5/3 law with a numerical constant 1.58, in good agreement with experiments. For a strong wind gradient, the spectrum in the production subrange has a k to the minus 1 law.

Tchen, C. M.↗