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At least 1,009 records · Page 56

PPPL Report on Reduced Modeling of Fusion Alpha Transport in ARC Burning Plasmas

We are reporting on the modeling of fusion alpha particle transport in the planned ARC fusion device being designed by the CFS (Commonwealth Fusion Systems: https://cfs.energy). The ARC tokamak is designed to operate in a burning-plasma regime characterized by a substantial population of fusion-born alpha particles. Alfvén eigenmode (AE) stability is assessed both analytically and numerically, incorporating alpha-particle drive, ion Landau, and radiative damping from thermal species and collisional damping from trapped electrons. Regions of unstable and near-threshold AE activity are mapped across ARC’s operational parameter space. Linear stability analysis with NOVA indicates multiple, often marginally unstable AEs, extending to toroidal mode numbers up to n= 30. The present report focuses on the ARC flat-top operating point prior to the sawtooth event. Alpha-particle transport on timescales exceeding the neoclassical slowing-down time is assessed using the NUBEAM module [1][2] of the TRANSP code [3], employing transport coefficients derived from the RBQ quasilinear modeling (cf. Appendix B). These global simulations identify favorable and unfavorable operating regimes with respect to alpha confinement, pressure redistribution, and overall alpha-heating efficiency. We also evaluate additional transport mechanisms—including neoclassical tearing mode (TM)–induced stochasticity, sawtooth-driven redistribution, and toroidal-field ripple using the kick model (cf. Appendix C) which makes use of the guiding-center code ORBIT, see Section 5. The kick model is integrated into TRANSP to enable self-consistent predictions of alpha-driven current formation and sustainment within the ARC scenario. Sensitivity scans are performed over the mode frequency, rational-surface alignment, island width, mode amplitude, and proximity of the limiter to the plasma. Our study provides an initial, physics-based guidance for machine design, operational planning, and equilibrium control, ensuring adequate alpha confinement and robust self-heating performance in ARC. Our simulations mostly targeted worst case scenarios, e.g. for TMs and sawteeth. Overall, we expect benign effects for the ARC scenario investigated in this work on fusion alpha confinement and losses in the presence of AEs, tearing modes and sawteeth. This report addresses three thrusts identified at the outset. The first thrust focuses on analytic estimates of the parametric dependencies of EP relaxation based on local AE stability simulations (Section 3). The second thrust involves global evaluations of AE stability using the NOVA, RBQ, and NUBEAM codes (Section 4). Finally, we investigate alpha-particle transport driven by low-frequency instabilities associated with sawteeth and tearing modes (Section 5).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The stability of steady motion of magnetic domain wall: Role of higher-order spin-orbit torques

The steady motion of magnetic domain wall driven by spin-orbit torques is investigated analytically in the heavy/ferromagnetic metal nanowires for three cases with a current transverse to the in-plane and perpendicular easy axis, and along the in-plane easy axis. By the stability analysis of Walker wall profile, we find that if including the higher-order spin-orbit torques, the Walker breakdown can be avoided in some parameter regions of spin-orbit torques with a current transverse to or along the in-plane easy axis. However, in the case of perpendicular anisotropy, even considering the higher-order spin-orbit torques, the velocity of domain wall cannot be efficiently enhanced by the current. Furthermore, the direction of wall motion is dependent on the configuration and chirality of domain wall with a current along the in-plane easy axis or transverse to the perpendicular one. Especially, the direction of motion can be controlled by the initial chirality of domain wall. So, if only involving the spin-orbit mechanism, it is preferable to adopt the scheme of a current along the in-plane easy axis for enhancing the velocity and controlling the direction of domain wall.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the stability conditions for theories of modified gravity in the presence of matter fields

We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagation for all the scalar modes. In case of tachyonic instability, the mass eigenvalues have been studied and we work out the appropriate expressions. For the latter, an instability occurs only when the negative mass eigenvalue is much larger, in absolute value, than the Hubble parameter. We discuss the results for the minimally coupled quintessence model showing for a particular set of parameters two typical behaviours which in turn lead to a stable and an unstable configuration. Moreover, we find that the speeds of propagation of the scalar modes strongly depend on matter densities, for the beyond Horndeski theories. Our findings can be directly employed when testing modified gravity theories as they allow to identify the correct viability space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Free-Flight CFD Simulations and Dynamic StabilityAnalysis of the Orion Crew Module

Dynamic stability analysis of the Multi-Purpose Crew Vehicle (MPCV) is performed us-ing the US3D flow solver and a plugin library to solve rigid-body dynamics, Free-Flight CFD(FF-CFD). Previous efforts investigated the free-flight behavior of higher speed, open-backaeroshell shapes. Three primary experimental sources are used to evaluate the predictivecapability of the FF-CFD solver in the low supersonic range (Mach≈1). First, the ballisticrange results obtained at the HFFAF facility at NASA Ames is used to verify the six degree-of-freedom (6-DoF) dynamic capability of the FF-CFD solver. Next, FF-CFD simulationsare preformed using restricted motion and the resultant trajectories are post-processed toobtain pitch damping coefficient as a function of angle-of-attack. The comparison of thepitch damping results obtained with one degree-of-freedom (1-DoF) FF-CFD compare wellwith experimental fits derived from ballistic range data. Finally, the atmospheric flight ca-pability of FF-CFD is compared to data from the Ascent Abort-2 (AA-2) flight experiment.Two simulations were performed using forced and forced-free flight to investigate surfacepressure predictive capability and free-flight aerodynamic performance through a varyingatmosphere at low speed (Mach 0.6-0.2). Surface pressure predicted with FF-CFD agreeswell with experimental trends, with slight over-prediction near the end of the trajectory.The total angle-of-attack for the free-flight portion agrees well with experimental data.

FFCFD↗

IMEX Runge-Kutta Parareal for Non-diffusive Equations

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear stability and convergence for IMEX Runge-Kutta Parareal methods on non-diffusive equations. By combining standard linear stability analysis with a simple convergence analysis, we find that certain Parareal configurations can achieve parallel speedup on non-diffusive equations. These stable configurations all posses low iteration counts, large block sizes, and a large number of processors. Numerical examples using the nonlinear Schrodinger equation demonstrate the analytical conclusions.

97 MATHEMATICS AND COMPUTING↗

Continuous and discrete modeling of HIV-1 decline on therapy

Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582–1586, 1996) and Perelson and Nelson (SIAM Rev 41:3–44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. Here, one of our main goals is to compare discrete mathematical models with the continuous model in Perelson et al. (1996) where HIV infected patients were given protease inhibitors and sampled frequently thereafter. For the comparison, we use experimental data collected in Perelson et al. (1996) and estimate the parameters such as the virion clearance rate and the rate of loss of infected cells by fitting the total concentration of plasma virus to this data set. Our results show that discrete systems describe the best fit. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. Motivated by Perelson and Nelson (1999), we end the paper with a mathematical model of imperfect protease inhibitor and reverse transcriptase (RT) inhibitor combination therapy of HIV-1 infection on time scales with its stability analysis.

60 APPLIED LIFE SCIENCES↗

AMOC sensitivity to surface buoyancy fluxes: Stronger ocean meridional heat transport with a weaker volume transport?

Oceanic northward heat transport is commonly assumed to be positively correlated with the Atlantic meridional overturning circulation (AMOC). For example, in numerical "water-hosing" experiments, imposing anomalous freshwater fluxes in the northern Atlantic leads to a slow-down of the AMOC and the corresponding reduction of oceanic northward heat transport. Here, we study the sensitivity of the ocean heat and volume transports to surface heat and freshwater fluxes using a generalized stability analysis. For the sensitivity to surface freshwater fluxes, we find that, while the direct relationship between the AMOC volume and heat transports holds on shorter time scales, it can reverse on timescales longer than 500 years or so. That is, depending on the model surface boundary conditions, reduction in the AMOC volume transport can potentially lead to a stronger heat transport on long timescales, resulting from the gradual increase in ocean thermal stratification. Finally, we discuss the implications of these results for the problem of steady state (statistical equilibrium) in ocean and climate GCM as well as paleoclimate problems including millennial climate variability.

54 ENVIRONMENTAL SCIENCES↗

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

36 MATERIALS SCIENCE↗

Dissipation-Induced Instabilities in Magnetized Flows

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. A hydrodynamically stable flow can be destabilized by the magnetic field both in an ideal and a viscous and resistive system giving rise to the azimuthal magnetorotational instability. A special solution to the equations of ideal magnetohydrodynamics characterized by the constant total pressure, the fluid velocity parallel to the direction of the magnetic field, and by the magnetic and kinetic energies that are finite and equal—the Chandrasekhar equipartition solution—is marginally stable in the absence of viscosity and resistivity. Performing a local stability analysis, we find the conditions under which the azimuthal magnetorotational instability can be interpreted as a dissipation-induced instability of the Chandrasekhar equipartition solution.

97 MATHEMATICS AND COMPUTING↗

Gaussian-type light bullet solutions of the (3+1)-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials

Two kinds of Gaussian-type light bullet (LB) solutions of the (3+1)-dimensional Schrödinger equation with cubic and power-law nonlinearities in PT-symmetric potentials are analytically obtained. The phase switches, powers and transverse power-flow densities of these solutions in homogeneous media are studied. The linear stability analysis of these LB solutions and the direct numerical simulation indicate that LB solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the defocusing cubic and focusing power-law nonlinear medium, while they are always unstable for all parameters in other media. Moreover, the broadened and compressed behaviors of LBs in the exponential periodic amplification system and diffraction decreasing system are discussed. Results indicate that LB is more stable for the sign-changing nonlinearity in the exponential periodic amplification system than for the non-sign-changing nonlinearity in the diffraction decreasing system at the same propagation distances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamics of bright–bright solitons in Bose–Einstein condensate with Raman-induced one-dimensional spin–orbit coupling

We investigate the dynamics of bright–bright solitons in one-dimensional two-component Bose–Einstein condensates with Raman-induced spin–orbit coupling, via the variational approximation and the numerical simulation of Gross–Pitaevskii equations. For the uniform system without trapping potential, we obtain two population balanced stationary solitons. By performing the linear stability analysis, we find a Goldstone eigenmode and an oscillation eigenmode around these stationary solitons. Moreover, we derive a general dynamical solution to describe the center-of-mass motion and spin evolution of the solitons under the action of spin–orbit coupling. The effects of a harmonic trap have also been discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamic consensus and extended high gain observers as a tool to achieve practical frequency synchronization in power systems under unknown time-varying power demand

In this paper, we consider the frequency synchronization problem in a network of lossless, connected, and network-reduced power system. Frequency synchronization is an important problem in power systems as frequency deviation can lead to degraded power quality, tripping of generators, etc. We present a load-estimator-based consensus algorithm in a network of fourth-order generator models that achieves practical frequency synchronization in the presence of unknown time-varying power demand. We do not assume that the demand is generated by a known model. We follow a multiple time-scale approach for the stability analysis. It is shown that synchronization is achieved for the case of constant power demand, by showing that the system is exponentially stable. Furthermore, for the case of time-varying power demand, we show the error trajectories are ultimately bounded, and the synchronization error is proportional to an upper bound on the derivative of the time-varying power demand. We simulate the controller performance on a four area network which is equivalent to the IEEE New England 39-Bus system.

42 ENGINEERING↗

Simulation of the properties of MgO-MgfCl{sub 2}-H{sub 2}O system by thermodynamic method

Magnesium oxychloride cement (MOC) has been investigated by many researchers who have studied its hydration products and properties. Previous works mainly concentrated on experimental studies. This study uses a thermodynamic approach to understand the formation conditions of two major hydration products of MOC, Mg{sub 3}(OH){sub 5}Cl · 4H{sub 2}O (phase 5) and Mg{sub 2}(OH){sub 3}Cl · 4H{sub 2}O (phase 3) at room temperature. The hydration reaction equilibrium of MOC phases has been predicted by using the geochemistry speciation code PHREEQC together with the extended ‘Pitzer.dat’ database. The results show that the formation of the hydration products are controlled by MgCl{sub 2} concentration, activity of H{sub 2}O and pH values of the system. The equilibrium of solid phase diagram, the solubility of different hydration phases are consistent with those results obtained from experimental studies, which validates the thermodynamic model. The phase diagram provides qualitative insights on the synthesis of pure phase 3 and phase 5. For MgO-MgCl{sub 2}-H{sub 2}O system, the minimum MgCl{sub 2} concentration for phase 5 and phase 3 to form are 1.47 mol · kg{sup −} {sup 1} and 2.25 mol · kg{sup −} {sup 1}, respectively. Increasing water volume can result in the transformation from phase 5 and phase 3 to brucite. Additionally, the stability analysis suggests that phase 5 prefers to formation at a higher condition of the a{sub Mg}2 +, pH and a{sub H2O} as compared to the phase 3. Phosphate can significantly influence the hydration products composition of MOC during hydration but no new phosphate appears. - Highlights: • A thermodynamic database was established for magnesium oxychloride cement system on the basis of Pitzer.dat. • Thermodynamic behaviors of magnesium oxychloride cement hydration was modeled. • Calculated phase diagram of magnesium oxychloride cement was plotted.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Three-dimensional explicit finite element formulation for shear localization with global tracking of embedded weak discontinuities

Shear localization is a damage mechanism characterized by the concentration of plastic deformation within thin bands of materials, often observed as a precursor to failure in metals. In this study, we present a three-dimensional explicit finite element formulation with embedded weak discontinuities for the treatment of shear localization under dynamic loading conditions. In this formulation, the onset of localization is detected via a material stability analysis suitable for rate-sensitive materials, and the continuity of propagating shear bands is ensured using a global tracking strategy involving a heat-conduction type boundary value problem, solved for a scalar level set function over the global domain of the problem. In addition, we propose a modified quadrature rule that is used to compute the contribution of an individual element to the global finite element arrays, taking into account the position of the embedded shear band within that element.

42 ENGINEERING↗

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)↗

Optimal scheduling and its Lyapunov stability for advanced load-following energy plants with CO 2 capture

In this study, a two-level control methodology consisting of an upper-level scheduler and a lower-level supervisory controller is proposed for an advanced load-following energy plant with CO 2 capture. With the use of an economic objective function that considers fluctuation in electricity demand and price at the upper level, optimal scheduling of energy plant electricity production and carbon capture with respect to several carbon tax scenarios is implemented. The optimal operational profiles are then passed down to corresponding lower-level supervisory controllers designed using a methodological approach that balances control complexity with performance. Finally, it is shown how optimal carbon capture and electricity production rate profiles for an energy plant such as the integrated gasification combined cycle (IGCC) plant are affected by electricity demand and price fluctuations under different carbon tax scenarios. As a result, the paper also presents a Lyapunov stability analysis of the proposed scheme.

01 COAL, LIGNITE, AND PEAT↗

A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes

In the present study, a spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. The spectral-difference Raviart-Thomas (SDRT) method was originally proposed by Balan et al. and implemented on triangular-element meshes for invisid flow only. Our present results demonstrated that the SDRT method is stable and high-order accurate in two dimensions (2D) for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes for both inviscid and viscous flows. A stability analysis is also performed for mixed elements. Furthermore, we found our current SDRT scheme is stable for fourth-order accurate spatial discretizations. However, a stable fifth-order SDRT scheme remains to be identified.

97 MATHEMATICS AND COMPUTING↗