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At least 271 records · Page 15

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING↗

Analytical closure to the spatially-filtered Euler equations for shock-dominated flows

To ensure numerical stability in the vicinity of shocks, a variety of methods have been used, including shock-capturing schemes such as weighted essentially non-oscillatory schemes, as well as the addition of artificial diffusivities to the governing equations. Centered finite difference schemes are often avoided near discontinuities due to the tendency for significant oscillations. However, such schemes have desirable conservation properties compared to many shock-capturing schemes. The objective of this work is to derive all necessary viscous/diffusion terms from first principles and then demonstrate the performance of these analytical terms within a centered differencing framework. The physical Euler equations are spatially-filtered with a Gaussian-like filter. Sub-filter scale (SFS) terms arise in the momentum and energy equations. Analytical closure is provided for each of them by leveraging the jump conditions for a shock. No SFS terms are present in the continuity or species equations. Here, this approach is tested for several problems involving shocks in one and two dimensions. Implemented within a centered difference code, the SFS terms perform well for a range of flow conditions without introducing excessive diffusion.

97 MATHEMATICS AND COMPUTING↗

Verification of an improved equation-free projective integration method for neoclassical plasma-profile evolution in tokamak geometry

A brute-force, long-time gyrokinetic simulation of plasma profile evolution in magnetic fusion devices is not desirable due to large computational resource requirements and a possible accumulation of numerical error. The equation-free projective integration method of Keverekidis et al. [Commun. Math. Sci. 1(4), 715–762 (2003)] is one of the outstanding candidates in projecting micro-scale simulations to a longer timescale. However, its application to tokamak plasma has not been fruitful due to the appearance of spurious transient oscillations in the lifting process, which are present when the kinetic simulations are initialized with a simplified model distribution function and which make the kinetic simulations to deviate from the desired paths. In this work, a kinetically informed lifting algorithm is added to the equation-free projective integration method, which is then verified in the electrostatic gyrokinetic particle-in-cell code XGCa [R. Hager and C. S. Chang, Phys. Plasmas 23, 042503 (2016)] for a neoclassical ion heat transport problem with adiabatic electrons. This new lifting operator is demonstrated to control spurious transients, enabling an over four-times reduction in the overall computing time in the time-evolution of the ion temperature profile in an axisymmetric toroidal plasma. Further reduction in the computing time is found to be limited due to the stability properties of the linear least squares projective integrator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

GEFSv12 High- and Low-Skill Day-10 Tornado Forecasts

Abstract On average, modern numerical weather prediction forecasts for daily tornado frequency exhibit no skill beyond day 10. However, in this extended-range lead window, there are particular model cycles that have exceptionally high forecast skill for tornadoes because of their ability to correctly simulate the future synoptic pattern. Here, model initial conditions that produced a more skillful forecast for tornadoes over the United States were exploited while also highlighting potential causes for low-skill cycles within the Global Ensemble Forecasting System, version 12 (GEFSv12). There were 88 high-skill and 91 low-skill forecasts in which the verifying day-10 synoptic pattern for tornado conditions revealed a western U.S. thermal trough and an eastern U.S. thermal ridge, a favorable configuration for tornadic storm occurrence. Initial conditions for high skill forecasts tended to exhibit warmer sea surface temperatures throughout the tropical Pacific Ocean and Gulf of Mexico, an active Madden–Julian oscillation, and significant modulation of Earth-relative atmospheric angular momentum. Low-skill forecasts were often initialized during La Niña and negative Pacific decadal oscillation conditions. Significant atmospheric blocking over eastern Russia—in which the GEFSv12 overforecast the duration and characteristics of the downstream flow—was a common physical process associated with low-skill forecasts. This work helps to increase our understanding of the common causes of high- or low-skill extended-range tornado forecasts and could serve as a helpful tool for operational forecasters. Significance Statement This research provides a framework for the anticipation of a more (or less) skillful 10-day tornado forecast in an operational numerical weather prediction system. High-skill forecasts were associated with substantial tropical convection and warm sea surface temperature throughout the Pacific Ocean and Gulf of Mexico, whereas the underlying cause of low-skill forecasts were typically associated with a blocking anticyclone over eastern Russia. These findings are important because they permit increased or decreased confidence in a long-range forecast of tornado occurrence based on a dynamical prediction system.

Meteorology & Atmospheric Sciences↗

Approximation of periodic Green's operator in real space using numerical integration and its use in fast Fourier transform-based micromechanical models

In this work, we propose an expression for the periodic first derivative of Green's function in real space. The proposed expression allows an alternative way of computing the periodic Green's operator based on periodically summing the free-space Green's operator in terms of an appropriate quadrature rule. We provide computational examples, which show the accuracy of the proposed approach, together with reduced spurious oscillations in the solution fields.

42 ENGINEERING↗

Quantum complexity of time evolution with chaotic Hamiltonians

We study the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator e -iHt whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion — the Eigenstate Complexity Hypothesis (ECH) — which bounds the overlap between offdiagonal energy eigenstate projectors and the k-local operators of the theory, and use it to argue that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-N SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with N = 2 fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE * BQP/poly and PSPACE * BQSUBEXP/subexp, and the “fast-forwarding” of quantum Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimum power analysis of a self-reactive wave energy point absorber with mechanically-driven power take-offs

This paper studies a self-reactive ocean wave energy converter (WEC) where energy is absorbed through the relative motion between a floating buoy on the ocean surface and a submerged body. Two types of direct-drive power take off (PTO) systems are examined. One adopts a ball screw system in inverse driving mode with mechanical motion rectifier (MMR) that converts the oscillating bi-directional input heave motion into unidirectional rotation to drive an electromagnetic generator, and another one uses a ball screw system to directly drive the generator (called non-MMR). Dynamic models for both types of PTOs are established and integrated with the overall WEC system model in both the time and frequency domains. Numerical simulation is used to investigate the dynamic performance of both PTOs. The influences of the PTO inerter, which is from the rotational inertia of the flywheel and generator, and the WEC drag damping coefficient are discussed and explored. The analytical closed-form solution for the optimum condition of the non-MMR system is derived based on the criterion of maximum power absorption, and numerical simulation yields the optimum condition for the MMR system. Overall, the results under regular and irregular waves show that the PTO inerter in the MMR system can improve the power absorption for small wave periods and maintain the same performance for large wave periods. The PTO inerter in the non-MMR system shifts the peak frequency. The WEC drag damping negatively influences the power absorption in both PTO systems, especially at large wave periods.

16 TIDAL AND WAVE POWER↗

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

Atomic force microscopy (AFM) is an important tool for measuring a variety of nanoscale surface properties, such as topography, viscoelasticity, electrical potential and conductivity. Some of these properties are measured using contact methods (static contact or intermittent contact), while others are measured using noncontact methods. Some properties can be measured using different approaches. Conductivity, in particular, is mapped using the contact-mode method. However, this modality can be destructive to delicate samples, since it involves continuously dragging the cantilever tip on the surface during the raster scan, while a constant tip–sample force is applied. In this paper we discuss a possible approach to develop an intermittent-contact conductive AFM mode based on Fourier analysis, whereby the measured current response consists of higher harmonics of the cantilever oscillation frequency. Such an approach may enable the characterization of soft samples with less damage than contact-mode imaging. To explore its feasibility, we derive the analytical form of the tip–sample current that would be obtained for attractive (noncontact) and repulsive (intermittent-contact) dynamic AFM characterization, and compare it with results obtained from numerical simulations. Although significant instrumentation challenges are anticipated, the modelling results are promising and suggest that Fourier-based higher-harmonics current measurement may enable the development of a reliable intermittent-contact conductive AFM method.

14 SOLAR ENERGY↗

An investigation of the multi-mode Richtmyer-Meshkov instability at a gas/HE interface using Pagosa

Here, in this work, we present a hydrocode Pagosa and explore the Richtmyer-Meshkov Instability (RMI) at an air/high explosive (HE) interface for the first time that is important but has not received much attention yet in the high explosive safety field. Thus, the presented Pagosa can be expected to predict the whole deflagration-to-detonation transition (DDT) process in future. In Pagosa, spatial discretization is implemented on cubic staggered grids by computing different variables at the vertex and the cell center, respectively, a special operator-splitting technique is employed to reduce the computational cost, and an artificial viscosity is added to handle the discontinuous shock waves in our simulations. To quantitatively evaluate the capability of Pagosa to solve these kinds of instabilities, the single mode Rayleigh-Taylor instability (RTI) and the multimode RMI at an air/SF 6 interface are first performed, respectively. The Pagosa results are compared with the related numerical solutions in the existing references and the experimental result. Moreover, a theoretical derivation of growth of RTI is also provided based on our numerical method. Subsequently, we explore the multi-mode RMI at an air/HE interface as well as the effects of several factors using Pagosa. Numerical results show that Pagosa is a powerful toolset to generate the right structures and the amplitude of RTI and RMI at an air/SF 6 interface. The solid HE can be penetrated by a strong shock wave and forms RMI deformations. The RMI at an air/HE interface behaves very different than at an air/SF 6 interface, periodic, decreased oscillation is observed due to material character, and is very sensitive to the initial simulation settings, that is, a tiny change in physical quantities will lead to a remarkable RMI structure, which is also observed in a shock bubble interaction. The findings in this work are significant, and will present a new insight for the high explosive field.

97 MATHEMATICS AND COMPUTING↗

Analysis of an induced Langmuir wave by ponderomotive forces and its applicability for plasma diagnostics

We present a numerical study on the electron and ion density perturbation in low-temperature plasmas driven by the frequency detuning of two intense laser beams. Our study is performed in the hydrodynamic regime, which becomes applicable when the plasma grating period induced by the beating of the laser beams is greater than the Debye length and collective processes such as plasma oscillations can be excited. Our findings show a resonance in electron density perturbation as the frequency detuning approaches a value consistent with the Bohm–Gross dispersion relation in low- and high-pressure plasmas. We discuss the potential of this resonance as a diagnostic tool for precisely measuring electron temperature and density in low-temperature plasmas through coherent scattering.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Preheating in Palatini Higgs inflation on the lattice

We study preheating following Higgs inflation in the Palatini formulation of gravity. We numerically evolve perturbations of the radial mode of the Higgs field and that of three scalars modeling the gauge bosons. We compare the two non-perturbative mechanisms of growth of excitations — parametric resonance and tachyonic instability — and confirm that the latter plays the dominant role. Our results provide further evidence that preheating in Palatini Higgs inflation happens within a single oscillation of the Higgs field about the bottom of its potential, consistent with the approximation of an instantaneous preheating.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Optical current generation in graphene: CEP control vs. ω + 2 ω control

The injection of directional currents in solids with strong optical fields has attracted tremendous attention as a route to realize ultrafast electronics based on the quantum-mechanical nature of electrons at femto- to attosecond timescales. Such currents are usually the result of an asymmetric population distribution imprinted by the temporal symmetry of the driving field. Here we compare two experimental schemes that allow control over the amplitude and direction of light-field-driven currents excited in graphene. Both schemes rely on shaping the incident laser field with one parameter only: either the carrier-envelope phase (CEP) of a single laser pulse or the relative phase between pulses oscillating at angular frequencies ω and 2ω, both for comparable laser parameters. We observe that the efficiency in generating a current via two-color-control exceeds that of CEP control by more than two orders of magnitude (7 nA vs. 18 pA), as the ω + 2ω field exhibits significantly more asymmetry in its temporal shape. We support this finding with numerical simulations that clearly show that two-color current control in graphene is superior, even down to single-cycle pulse durations. We expect our results to be relevant to experimentally access fundamental properties of any solid at ultrafast timescales, as well as for the emerging field of petahertz electronics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Amazon and La Plata River Basins as Moisture Sources of South America: Climatology and Intraseasonal Variability

Abstract Land‐atmosphere interactions are critical for precipitation (PPT) over South America where terrestrial evapotranspiration (ET) constitutes a significant fraction of moisture for rainfall over the ecologically and socio‐economically vital Amazon (AMZ) and La Plata (LPB) river basins. We quantify the contribution of ET from AMZ and LPB to PPT over the continent with a focus on the intraseasonal time scale. Using numerical water tracers embedded in the Weather Research and Forecasting model we track the moisture originating from the two basins. Our findings indicate that approximately 40% of annual rainfall over the eastern foothills of the Andes originates as AMZ ET, and nearly 30% of rainfall over northern Argentina originates as LPB ET. Analysis of moisture transport during both phases of the dominant intraseasonal oscillation pattern over South America reveals an intraseasonal “sloshing” of LPB moisture between the South Atlantic convergence zone (SACZ) and southeastern South America (SESA) regions. AMZ and LPB each supply approximately 6% of moisture for SACZ PPT during periods of intraseasonal enhancement (positive anomalies), highlighting the importance of moisture from the Atlantic Ocean. For the SESA region, LPB supplies 26% of the moisture for PPT during periods of intraseasonal enhancement while AMZ supplies 5%.

54 ENVIRONMENTAL SCIENCES↗

Cooling and instabilities in colliding flows

ABSTRACT Collisional self-interactions occurring in protostellar jets give rise to strong shocks, the structure of which can be affected by radiative cooling within the flow. To study such colliding flows, we use the AstroBEAR AMR code to conduct hydrodynamic simulations in both one and three dimensions with a power-law cooling function. The characteristic length and time-scales for cooling are temperature dependent and thus may vary as shocked gas cools. When the cooling length decreases sufficiently and rapidly, the system becomes unstable to the radiative shock instability, which produces oscillations in the position of the shock front; these oscillations can be seen in both the one- and three-dimensional cases. Our simulations show no evidence of the density clumping characteristic of a thermal instability, even when the cooling function meets the expected criteria. In the three-dimensional case, the nonlinear thin shell instability (NTSI) is found to dominate when the cooling length is sufficiently small. When the flows are subjected to the radiative shock instability, oscillations in the size of the cooling region allow NTSI to occur at larger cooling lengths, though larger cooling lengths delay the onset of NTSI by increasing the oscillation period.

79 ASTRONOMY AND ASTROPHYSICS↗

Review of Wave Energy Converter Power Take-Off Systems, Testing Practices, and Evaluation Metrics: Preprint

While the field of wave energy has been the subject of numerical simulation, scale model testing, and precommercial project testing for decades, wave energy technologies remain in the early stages of development and must continuing proving themselves as a promising modern renewable energy field. One of the difficulties that wave energy systems have been struggling to overcome is the design of highly efficient energy conversion systems that can convert the mechanical power, derived from the oscillation of wave activated bodies, into another useful product. Often the power take-off (PTO) is defined as the single unit responsible for converting mechanical power into another usable form such as electricity, pressurized fluid, compressed air, and others. The PTO, and the entire power conversion chain (PCC), is of great importance as it affects not only how efficient wave power is converted into electricity, but also contributes to the mass, size, structural dynamics, and levelized cost of energy (LCOE) of the wave energy converter (WEC). Unlike wind and solar, there is no industrial standard device, or devices, for wave energy conversion and this diversity is transferred to the PTO system. The majority of current WEC PTO systems incorporate a mechanical or hydraulic drive train, power generator, and an electrical control system. The challenge of WEC PTO designs is designing a mechanical-to-electrical component that can efficiently convert irregular, bi-directional, low frequency and low alternating velocity wave motions. While gross average power levels can be predicted in advance, the variable wave elevation input has to be converted into smooth electrical output and hence usually necessitates some type of energy storage system, such as battery storage, accumulator super capacitors, etc., or other means of compensation such as an array of devices. One of the primary challenges for wave energy converter systems is the fluctuating nature of wave resources, which require WEC components to be designed to handle loads (i.e. torques, forces, and powers) that are many times greater than the average load. This approach requires a much greater PTO capacity than the average power output and indicates a higher cost. In addition, supporting mechanical coupling and or gearing can be added to the PCC to help alleviate the difficulties with transmission and control of fluctuating large loads with low frequencies (indicative of wave forcing) into smaller loads at higher frequencies (optimum for conventional electrical machine design) can quickly increase the complexity of the PCC which could result in a greater number of failure modes and increased maintenance costs. All of the previous points demonstrate how the PTO influences WEC dynamics, reliability, performance and cost which are critical design factors. This paper further explores these topics by providing a review of the state-of-the-art PTO systems currently under development, how these novel PTO systems are tested and derisked prior to precommercial deployment, and the evaluation metrics historically used to differentiate between PTO designs and how they can be improved to support control co-design focused development of wave energy systems.

laboratory testing↗

A weighted shifted boundary method for immersed moving boundary simulations of Stokes' flow

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. Here, in this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.

97 MATHEMATICS AND COMPUTING↗

Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping

Here, we study the one-dimensional nearest-neighbor tight-binding model of electrons with independently distributed random hopping and no on-site potential (i.e., off-diagonal disorder with particle-hole symmetry, leading to sublattice symmetry, for each realization). For nonsingular distributions of the hopping, it is known that the model exhibits a universal, singular behavior of the density of states $ρ(E) ~ 1/|E\: \text{ln}^3 |E||$ and of the localization length $ξ(E) ~ |\text{ln}|E||$, near the band center $\textit{E}$ = 0 . (This singular behavior is also applicable to random $\textit{XY}$ and Heisenberg spin chains; it was first obtained by Dyson for a specific random harmonic oscillator chain.) Simultaneously, the state at$\textit{E}$ = 0 shows a universal, subexponential decay at large distances $\sim \text{exp}[–\sqrt{r/r_0}]$. In this study, we consider singular, but normalizable, distributions of hopping, whose behavior at small $\textit{t}$ is of the form $\sim 1/[t \text{ln}^{λ+1}(1/t)]$, characterized by a single, continuously tunable parameter λ > 0. We find, using a combination of analytic and numerical methods, that while the universal result applies for λ > 2, it no longer holds in the interval 0 < λ < 2. In particular, we find that the form of the density of states singularity is enhanced (relative to the Dyson result) in a continuous manner depending on the nonuniversal parameter λ; simultaneously, the localization length shows a less divergent form at low energies and ceases to diverge below λ = 1. For λ < 2, the fall-off of the $\textit{E}$ = 0 state at large distances also deviates from the universal result and is of the form $\sim\text{exp}[–(r/r_0)^{1/λ}]$ , which decays faster than an exponential for λ < 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗