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Here, this paper presents a closure to “Observation-Based Evaluation of Flood Estimation Techniques for a Small Snow-Dominated Basin in the Washington Cascade Mountains” by Hongxiang Yan, Zhuoran Duan, Mark S. Wigmosta, Ning Sun, Ethan D. Gutmann, Bert Kruyt, and Jeffrey R. Arnold. https://doi.org/10.1061/JHYEFF .HEENG-6147.
Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here, we numerically study the conditions under which the MA equations yield results reflecting the true stochastic dynamics of the system. We show that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the chemical master equation, only when the steady-state mean molecule numbers obtained from the chemical master equation fall within a certain finite range. The same validity criterion for monostable systems implies that the steady-state mean molecule numbers obtained from the chemical master equation must be above a certain threshold. For mean molecule numbers outside of this range of validity, the MA equations lead to either qualitatively wrong oscillatory dynamics or to unphysical predictions such as negative variances in the molecule numbers or multiple steady-state moments of the stationary distribution as the initial conditions are varied. Our results clarify the range of validity of the MA approach and show that pitfalls in the interpretation of the results can only be overcome through the systematic comparison of the solutions of the MA equations of a certain order with those of higher orders.
Ion parallel closures are obtained for arbitrary atomic weights and charge numbers. For arbitrary collisionality, the heat flow and viscosity are expressed as kernel-weighted integrals of the temperature and flow-velocity gradients.
Results presented here are from 6-field Landau-Fluid simulations using shifted circular cross-section tokamak equilibria on BOUT++ framework. Linear benchmark results imply that the collisional and collisionless Landau resonance closures make a little difference on linear growth rate spectra which are quite close to the results with the flux limited Spitzer-Härm parallel flux. Both linear and nonlinear simulations show that the plasma current profile plays dual roles on the peeling-ballooning modes that it can drive the low-n peeling modes and stabilize the high-n ballooning modes. For fixed total pressure and current, as the pedestal current decreases due to the bootstrap current which becomes smaller when the density (collisionality) increases, the operational point is shifted downwards vertically in the J ped – α diagram, resulting in threshold changes of different modes. In conclusion, the bootstrap current can slightly increase radial turbulence spreading range and enhance the energy and particle transports by increasing the perturbed amplitude and broadening cross-phase frequency distribution.
Here, we describe mathematical methods based on optimizing a modified non-linear flux function (MFF) to evaluate whether odd-parity perturbations affect the local closure of magnetic field lines in field-reversed configurations. Using the MFF methodology, quantitative formulas are derived that provide the shift of the field minimum and the threshold for field-line opening, a discontinuous change in field topology.
A closure model for turbulent flows is developed based on a dynamical system theory. An appropriately discretized formulation of the governing equations is considered for this process. The key ingredient is an approximation of the system’s attractor, where all the trajectories in phase space are confined. This approximate inertial manifold based approach provides a path to track trajectories of the system in a lower-dimensional subspace. Unlike conventional coarse-graining approaches, the turbulent field is decomposed into resolved and unresolved dynamics using the properties of the governing equations. The novelty of the approach relies on the reconstruction of the unresolved field constrained by the governing equations. A posteriori tests for homogeneous isotropic turbulence and the Kuramoto–Sivashinsky equation show promising results for considerable dimension reduction with strong convergence properties. The proposed model outperforms the dynamic Smagorinsky model, and the computational overhead is competitive with similar approaches.
We develop a theory for the cascade mixing terms in a moment closure approach to binary active scalar mixing in variable-density turbulence. To address the variable-density complications we apply, as a principle and constraint, the conservation of the probability density function (PDF) through a Fokker–Planck equation with bounded sample space whose attractor is the beta PDF with skewness. Mixing is related to a single-point PDF as a realisability principle to provide mathematically rigorous expressions for the small scale statistics in terms of largescale moments. The problem of the unknown small-scale mixing is replaced with the determination of the drift and diffusion terms of a Fokker–Planck equation in a beta-PDF-convergent stochastic process. We find that realisability of a beta-convergent process requires the mixing time-scale ratio, taken as a constant in passive scalar mixing, to be a function of the mean mass fraction, mean fluid density, the Atwood number, the density-volume correlation and moments of the density field. We develop and compare the new model with direct numerical simulations data of non-stationary homogeneous variable-density turbulence.
We demonstrate a new technique for detecting radio transients based on interferometric closure quantities. The technique uses the bispectrum, the product of visibilities around a closed loop of baselines of an interferometer. The bispectrum is calibration independent, resistant to interference, and computationally efficient, so it can be built into correlators for real-time transient detection. Our technique could find celestial transients anywhere in the field of view and localize them to arcsecond precision. At the Karl G. Jansky Very Large Array (VLA), such a system would have a high survey speed and a 5{sigma} sensitivity of 38 mJy on 10 ms timescales with 1 GHz of bandwidth. The ability to localize dispersed millisecond pulses to arcsecond precision in large volumes of interferometer data has several unique science applications. Localizing individual pulses from Galactic pulsars will help find X-ray counterparts that define their physical properties, while finding host galaxies of extragalactic transients will measure the electron density of the intergalactic medium with a single dispersed pulse. Exoplanets and active stars have distinct millisecond variability that can be used to identify them and probe their magnetospheres. We use millisecond timescale visibilities from the Allen Telescope Array and VLA to show that the bispectrum can detect dispersed pulses and reject local interference. The computational and data efficiency of the bispectrum will help find transients on a range of timescales with next-generation radio interferometers.
A large-volume flux closure during transient coaxial helicity injection (CHI) in NSTX-U is demonstrated through resistive magnetohydrodynamics (MHD) simulations. Several major improvements, including the improved positioning of the divertor poloidal field coils, are projected to improve the CHI start-up phase in NSTX-U. Simulations in the NSTX-U configuration with constant in time coil currents show that with strong flux shaping the injected open field lines (injector flux) rapidly reconnect and form large volume of closed flux surfaces. This is achieved by driving parallel current in the injector flux coil and oppositely directed currents in the flux shaping coils to form a narrow injector flux footprint and push the injector flux into the vessel. As the helicity and plasma are injected into the device, the oppositely directed field lines in the injector region are forced to reconnect through a local Sweet-Parker type reconnection, or to spontaneously reconnect when the elongated current sheet becomes MHD unstable to form plasmoids. In these simulations for the first time, it is found that the closed flux is over 70% of the initial injector flux used to initiate the discharge. Furthermore, these results could work well for the application of transient CHI in devices that employ super conducting coils to generate and sustain the plasma equilibrium.
Here, energetic particle populations in nuclear fusion experiments can destabilize the Alfvén Eigenmodes through inverse Landau damping and couplings with gap modes in the shear Alfvén continua. We use the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles. We add the Landau damping and resonant destabilization effects using a closure relation. We apply the model to study the Alfvén mode stability in the inward-shifted configurations of the Large Helical Device (LHD), performing a parametric analysis of the energetic particle β (${{\beta}_{f}}$ ) in a range of realistic values, the ratios of the energetic particle thermal/Alfvén velocities (${{V}_{\text{th}}}/{{V}_{A0}}$ ), the magnetic Lundquist numbers (S) and the toroidal modes (n). The n = 1 and n = 2 TAEs are destabilized, although the n = 3 and n = 4 TAEs are weakly perturbed. The most unstable configurations are associated with the density gradients of energetic particles in the plasma core: the TAEs are destabilized, even for small energetic particle populations, if their thermal velocity is lower than 0.4 times the Alfvén velocity. The frequency range of MHD bursts measured in the LHD are 50–70 kHz for the n = 1 and 60–80 kHz for the n = 2 TAE, which is consistent with the model predictions.
Alfvén Eigenmodes (AE) can be destabilized by energetic particles in neutral beam injection (NBI) heated plasmas through inverse Landau damping and couplings with gap modes in the shear Alfvén continua. In this paper, we describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system using the reduced MHD equations, density and parallel velocity moments for the energetic particles as well as the geodesic acoustic wave dynamics. A closure relation adds the Landau damping and resonant destabilization effects in the model. We apply the model to study the Alfvén modes stability in TJ-II, performing a parametric analysis in a range of realistic values of energetic particle β ($\beta_{f}$ ), ratios of thermal/Alfvén velocities ($V_{\rm th}/V_{\rm A0}$ ), energetic particle density profiles and toroidal modes (n) including toroidal and helical couplings. The study predicts a large helical coupling between different toroidal modes and the destabilization of helical Alfvén eigenmodes (HAE) with frequencies similar to the AE activity measured in TJ-II, between 50–400 kHz. The analysis has also revealed the destabilization of GAE (global Alfvén eigenmodes), TAE (toroidal Alfvén eigenmodes) and EPM (energetic particle modes). For the modes considered here, optimized TJ-II operations require a $\rlap{-} \iota$ profile in the range of $[0.845, 0.979]$ to stabilize AEs in the inner and middle plasma. AEs in the plasma periphery cannot be fully stabilized, although for a configuration with $\rlap{-} \iota = [0.945, 1.079]$ , only $n=7, 11, 15$ AE are unstable with a growth rate 4 times smaller compared to the standard $\rlap{-} \iota = [1.54, 1.68]$ case and a frequency of 100 kHz. Finally, we reproduce the frequency sweeping evolution of the AE frequency observed in TJ-II as the $\rlap{-} \iota$ profile is varied. The AE frequency sweeping is caused by consecutive changes of the instability dominant modes between different helical families.
The aim of this study is to perform a theoretical analysis of the magnetohydrodynamic (MHD) stability and energetic particle effects on a LHD equilibria, calculated during a discharge where energetic-ion-driven resistive interchange mode (EIC) events were triggered. Here, we use the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species, including the effect of the acoustic modes, multiple energetic particles (EP) species, helical couplings and helically trapped EP. We add the Landau damping and resonant destabilization effects using a closure relation. The simulations suggest that the helically trapped EP driven by the perpendicular neutral beam injector (NBI) further destabilizes the 1/1 MHD-like mode located at the plasma periphery ( r / a = 0.88). If the β of the EP driven by the perpendicular NBI is larger than 0.0025 a 1/1 EIC with a frequency around 3 kHz is destabilized. If the effect of the passing EP driven by the tangential NBI is included on the model, any enhancement of the injection intensity of the tangential NBI below β leads to a decrease of the instability growth rate. The simulations indicate that the perpendicular NBI EP is the main driver of the EIC events, as it was observed in the experiment. If the effect of the helical couplings are added in the model, an 11/13 EIC is destabilized with a frequency around 9 kHz, inward shifted ( r / a = 0.81) compared to the 1/1 EIC. Thus, one possible explanation for the EIC frequency chirping down from 9 to 3 kHz is a transition between the 11/13 to the 1/1 EIC due to a weakening of the destabilizing effect of the high n modes, caused by a decrease of the EP drive due to a loss of helically trapped EP or a change in the EP distribution function after the EIC burst. The experimental data during the EIC bursting phase shows a complex mode structure and an inward shift of the instability, although no direct evidence of the proposed transition has been observed yet.
The aim of this study is to analyze the stability of the Alfven eigenmodes (AE) in the Chinese First Quasi-axisymmetric Stellarator (CFQS). The AE stability is calculated using the code FAR3d that solves the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moment for the energetic particles (EP) species including the effect of the helical couplings and acoustic modes. The Landau damping and resonant destabilization effects are added in the model by a given closure relation. The simulation results indicate the destabilization of n = 1 to 4 AEs by EP during the slowing down process, particularly n = 1 and n = 2 toroidal AEs (TAE), n = 3 elliptical AE (EAE) and n = 4 non circular AE (NAE). If the resonance is caused by EPs with an energy above 17 keV (weakly thermalized EP), n = 2 EAEs and n = 3 NAEs are unstable. On the other hand, EPs with an energy below 17 keV (late thermalization stage) lead to the destabilization of n = 3 and n = 4 TAEs. The simulations for an off-axis NBI injection indicate the further destabilization of n = 2 to 4 AEs although the growth rate of the n = 1 AEs slightly decreases, so no clear optimization trend with respect to the NBI deposition region is identified. In addition, n = 2, 4 helical AE (HAE) are unstable above an EP β threshold. Also, if the thermal β of the simulation increases (higher thermal plasma density) the AE stability of the plasma improves. Overall, the simulations including the effect of the finite Larmor radius and electron-ion Landau damping show the stabilization of the n = 1 to 4 EAE/NAEs as well as a decrease of the growth rate and frequency of the n = 1 to 4 BAE/TAEs.
Abstract Energetic particle (EP) destabilized Alfvén eigenmode (AE) instabilities are simulated for a DIII-D experimental case with a pulsed neutral beam using a gyro-Landau moments model which introduces EP phase-mixing effects through closure relations. This provides a computationally efficient reduced model which is applied here in the nonlinear regime over timescales that would be difficult to address with more complete models. The long timescale nonlinear evolution and related collective transport losses are examined including the effects of zonal flow/current generation, nonlinear energy cascades, and EP profile flattening. The model predicts frequencies and mode structures that are consistent with experimental observations. These calculations address issues that have not been considered in previous modelling: the EP critical gradient profile evolution in the presence of zonal flows/currents, and the dynamical nature of the saturated state. A strong level of intermittency is present in the predicted instability-driven transport; this is connected to the zonal flow growth and decay cycles and nonlinear energy transfers. Simulation of intermittent AE-enhanced EP transport will be an important issue for the protection of plasma facing components in the next generation of fusion devices.
Stably stratified turbulence (SST), a model that is representative of the turbulence found in the oceans and atmosphere, is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying scenarios. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations—used to numerically simulate approximate solutions for such turbulent flows. Rather than attempting to model each term in URANS separately, it is attractive to explore the capability of machine learning (ML) to model groups of terms, i.e. to directly model the force balances. We develop deep time-series ML for closure modeling of the URANS equations applied to SST. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: long short-term memory and neural ordinary differential equation. Both models perform accurately and are numerically stable in a posteriori (online) tests. Furthermore, we explore the data requirements of the time-series ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of high-dimensional complex dynamical system like SST flows.
Here, the high spin excited states of Lanthanum isotopes 140–143 La, above the 𝑁 = 82 closed shell, were populated in fission reactions. The prompt 𝛾-ray transitions were measured using two complementary methods: (a) in coincidence with the isotopically identified fragments produced in the fission of the 238 U + 9 Be system using the Variable Mode Spectrometer (VAMOS++) and the Advanced Gamma Tracking Array (AGATA) spectrometer, and (b) high statistics threefold 𝛾−𝛾−𝛾 and fourfold 𝛾−𝛾−𝛾−𝛾 coincidence data from the spontaneous fission of 252 Cf using the Gammasphere. This work reports the first identification of a pair of parity doublet structures in 143 La and the new high spin level structure in 140–142 La from prompt 𝛾-ray spectroscopy. The level structures are interpreted in terms of the systematics of neighboring odd-𝑍 nuclei above the 𝑍 = 50 shell closure and large-scale shell model calculations. The present results indicate the presence of stable octupole deformation in 143 La. The excitation energy pattern and their comparison with neighboring isotones, moving away from the 𝑁 = 82 closed shell, point towards a transition from single-particle structures to an alternating parity rotational band structure in the La isotopic chain.
Here, using quantum Monte Carlo (QMC) calculations, we investigate the insulator-metal transition observed in liquid hydrogen at high pressure. Below the critical temperature of the transition from the molecular to the atomic liquid, the fundamental electronic gap closure occurs abruptly, with a small discontinuity reflecting the weak first-order transition in the thermodynamic equation of state. Above the critical temperature, molecular dissociation sets in while the gap is still open. When the gap closes, the decay of the off-diagonal reduced density matrix shows that the liquid enters a gapless, but localized, phase: there is a crossover between the insulating and the metallic liquids. Compared to different density functional theory (DFT) functionals, our QMC calculations provide larger values for the fundamental gap and the electronic density of states close to the band edges, indicating that optical properties from DFT potentially benefit from error cancellations.
The equations of state and band-gap closures for Pb Cl 2 and Sn Cl 2 were studied using both experimental and theoretical methods. Here we measured the volume of both materials to a maximum pressure of 70 GPa using synchrotron-based angle-dispersive powder x-ray diffraction. The lattice parameters for both compounds showed anomalous changes between 16–32 GPa, providing evidence of a phase transition from the cotunnite structure to the related Co 2 Si structure, in contrast to the postcotunnite structure as previously suggested. First-principles calculations confirm this finding and predict a second phase transition to a Co 2 Si-like structure between 75– 110 GPa in Pb Cl 2 and 60–75 GPa in Sn Cl 2 . Band gaps were measured under compression to ~70 GPa for Pb Cl 2 and ~66 GPa for Sn Cl 2 and calculated up to 200 GPa for Pb CI 2 and 120 GPa for Sn Cl 2 . We find an excellent agreement between our experimental and theoretical results when using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional, which suggests that this functional could reliably be used to calculate the band gap of similar AX 2 compounds. Experimental and calculated band-gap results show discontinuous decreases in the band gap corresponding to phase changes to higher-coordinated crystal structures, giving insight into the relationship between interatomic geometry and metallicity.