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At least 1,387 records · Page 77

Continental United States may lose 1.8 petagrams of soil organic carbon under climate change by 2100

Abstract Aims High‐resolution information on soils’ vulnerability to climate‐induced soil organic carbon (SOC) loss can enable environmental scientists, land managers, and policy makers to develop targeted mitigation strategies. This study aims to estimate baseline and decadal changes in continental US surface SOC stocks under future emission scenarios. Location Continental United States. Time period 2014–2100. Methods We used recent SOC field observations ( n = 6,213 sites), environmental factors ( n = 32), and an ensemble machine learning (ML) approach to estimate baseline SOC stocks in surface soils across the continental United States at 100‐m spatial resolution, and decadal changes under the projected climate scenarios of Coupled Model Intercomparison Project Phase Six (CMIP6) earth system models (ESMs). Results Baseline SOC projections from ML approaches captured more than 50% of variability in SOC observations, whereas ESMs represented only 6–16% of observed SOC variability. ML estimates showed a mean total loss of 1.8 Pg C from US surface soils under the high‐emission scenario by 2100, whereas ESMs showed no significant change in SOC stocks with wide variation among ESMs. Both ML and ESM predictions agree on the direction of SOC change (net emissions or sequestration) across 46–51% of continental US land area. These differences are attributable to the high‐resolution site‐specific data used in the ML models compared to the relatively coarse grid represented in CMIP6 ESMs. Main conclusions Our high‐resolution estimates of baseline SOC stocks, identification of key environmental controllers, and projection of SOC changes from US land cover types under future climate scenarios suggest the need for high‐resolution simulations of SOC in ESMs to represent the heterogeneity of SOC. We found that the SOC change is sensitive to key soil related factors (e.g. soil drainage and soil order) that have not been historically considered as input parameters in ESMs, because currently more than 95% variability in the SOC of CMIP6 ESMs is controlled by net primary productivity, temperature, and precipitation. Using additional environmental factors to estimate the baseline SOC stocks and predict the future trajectory of SOC change can provide more accurate results.

54 ENVIRONMENTAL SCIENCES↗

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗

Nonlinear dynamics of global atmospheric and Earth-system processes

Researchers are continuing their studies of the nonlinear dynamics of global weather systems. Sensitivity analyses of large-scale dynamical models of the atmosphere (i.e., general circulation models i.e., GCM's) were performed to establish the role of satellite-signatures of soil moisture, sea surface temperature, snow cover, and sea ice as crucial boundary conditions determining global weather variability. To complete their study of the bimodality of the planetary wave states, they are using the dynamical systems approach to construct a low-order theoretical explanation of this phenomenon. This work should have important implications for extended range forecasting of low-frequency oscillations, elucidating the mechanisms for the transitions between the two wave modes. Researchers are using the methods of jump analysis and attractor dimension analysis to examine the long-term satellite records of significant variables (e.g., long wave radiation, and cloud amount), to explore the nature of mode transitions in the atmosphere, and to determine the minimum number of equations needed to describe the main weather variations with a low-order dynamical system. Where feasible they will continue to explore the applicability of the methods of complex dynamical systems analysis to the study of the global earth-system from an integrative viewpoint involving the roles of geochemical cycling and the interactive behavior of the atmosphere, hydrosphere, and biosphere.

Saltzman, Barry↗

Conservative-coordinate transformations for atmospheric measurements

This lecture describes a technique by which atmospheric measurements of trace species with medium to long lifetimes can be 'coincidentally' compared and validated even though measurements are taken at different locations and different times In other words, the method, under suitable counditions, can remove a large amount of the natural meteorological variability. The technique involves the use of quasi-Lagrangian or conservative coordinates - air parcel tags which are invariant or nearly invariant under the motion of the parcel. The technique is called 'reconstruction', since measurements taken at one location can be reconstructed at different locations. In order to do this, the data are transformed into the conservative coordinates and accumulated. Within the conservative reference frame, much of the meteorological variability is removed. Once enough data are obtained within the system, the observations can be tranformed back into physical space at any location and compared with other measurements. The method by which the trace species data are obtained makes no difference; satellite, balloon, rocket, aircraft and ground-based data all become equivalent and can be intercompared. The conservative-coordinate system not only allows for intercomparison of data, but shows how data can be taken in such a way as to maximize the physical scope of the information. In other words, the method automatically suggests when conditions might be suitable to obtain information with different environmental situations. It also allows for the forecast of constituent fields using only the meteorological forecasts and limited observational data.

Schoeberl, M. R.↗

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗

Optimization of Supersonic Transport Trajectories

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Ardema, Mark D.↗

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Ardema, Mark D.↗

Precision DIS thrust predictions for HERA and EIC

We present predictions for the DIS 1-jettiness event shape $τ^b_1$, or DIS thrust, using the framework of Soft Collinear Effective Theory (SCET) for factorization, resummation of large logarithms, and rigorous treatment of nonperturbative power corrections, matched to fixed-order QCD away from the resummation region. Our predictions reach next-to-next-to-next-to-leading-logarithmic (N 3 LL) accuracy in resummed perturbation theory, matched to $\mathcal{O}(α^2_s)$ fixed-order QCD calculations obtained using the program NLOJet++. We include a rigorous treatment of hadronization corrections, which are universal across different event shapes and kinematic variables x and Q at leading power, and supplement them with a systematic scheme to remove $\mathcal{O}$(Λ QCD ) renormalon ambiguities in their definition. The framework of SCET allows us to connect smoothly the nonperturbative, resummation, and fixed-order regions, whose relative importance varies with x and Q, and to rigorously estimate theoretical uncertainties, across a broad range of x and Q covering existing experimental results from HERA as well as expected new measurements from the upcoming Electron- Ion-Collider (EIC). Our predictions will serve as an important benchmark for the EIC program, enabling the precise determination of the QCD strong coupling α s and the universal nonperturbative first moment parameter Ω 1 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Preliminary Assessment of Variable Speed Power Turbine Technology on Civil Tiltrotor Size and Performance

A Large Civil Tiltrotor (LCTR) conceptual design was developed as part of the NASA Heavy Lift Rotorcraft Systems Investigation in order to establish a consistent basis for evaluating the benefits of advanced technology for large tiltrotors. The concept has since evolved into the second-generation LCTR2, designed to carry 90 passengers for 1,000 nm at 300 knots, with vertical takeoff and landing capability. This paper performs a preliminary assessment of variable-speed power turbine technology on LCTR2 sizing, while maintaining the same, advanced technology engine core. Six concepts were studied; an advanced, single-speed engine with a conventional power turbine layout (Advanced Conventional Engine, or ACE) using a multi-speed (shifting) gearbox. There were five variable-speed power turbine (VSPT) engine concepts, comprising a matrix of either three or four turbine stages, and fixed or variable guide vanes; plus a minimum weight, twostage, fixed-geometry VSPT. The ACE is the lightest engine, but requires a multi-speed (shifting) gearbox to maximize its fuel efficiency, whereas the VSPT concepts use a lighter, fixed-ratio gearbox. The NASA Design and Analysis of Rotorcraft (NDARC) design code was used to study the trades between rotor and engine efficiency and weight. Rotor performance was determined by Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics (CAMRAD II), and engine performance was estimated with the Numerical Propulsion System Simulation (NPSS). Design trades for the ACE vs. VSPT are presented in terms of vehicle gross and empty weight, propulsion system weight and mission fuel burn for the civil mission. Because of its strong effect on gearbox weight and on both rotor and engine efficiency, rotor speed was chosen as the reference design variable for comparing design trades. Major study assumptions are presented and discussed. Impressive engine power-to-weight and fuel efficiency reduced vehicle sensitivity to propulsion system choice. The 10% weight penalty for multi-speed gearbox was more significant than most engine technology weight penalties to the vehicle design because drive system weight is more than two times engine weight. Based on study assumptions, fixed-geometry VSPT concept options performed better than their variable-geometry counterparts. Optimum design gross weights varied 1% or less and empty weights less than 2% among the concepts studied, while optimum fuel burns varied up to 5%. The outcome for some optimum configurations was so unexpected as to recommend a deeper look at the underlying technology assumptions.

Snyder, Christopher A.↗

Annotations on the virtual element method for second-order elliptic problems

This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the numerical discretization of Partial Differential Equations (PDEs) and, in particular, the Finite Element Method (FEM). This document is not an introduction to the FEM, for which many textbooks (also free on the internet) are available. Eventually, this document is intended to evolve into a tutorial introduction to the VEM (but this is really a long-term goal).

97 MATHEMATICS AND COMPUTING↗

Seasat altimeter determination of ocean current variability

An experiment conducted in the Kuroshio Current, east of Japan, has confirmed the ability of radar altimeters of precision on the order of 10 cm, such as that of the Seasat satellite, to measure the small oceanic height variations associated with geostrophic ocean currents. Changes in surface dynamic height were inferred from data gathered by air-expendable barithermographs, which had been dropped to coincide with the Seasat subtrack, for the periods between the flights of September 25 and October 5 and 13, 1978. The changes registered generally agreed to within + or - 10 cm of the height changes observed in the altimeter data.

Bernstein, R. L.↗

The elusive variability of BD + 10.2179 deg

High-speed photometry of the hydrogen-deficient star BD + 10.2179 deg has been obtained in order to ascertain if it is presently pulsationally unstable with the previously published period of 0.162 to 0.164 d. During an observing run of 0.21 d no pulsations were observed above the noise limit of 0.002 mag. Either the previously published period is not real or the star is no longer pulsating.

Drilling, J. S.↗

Antiferroelectric Phase Transition in a Proton-Transfer Salt of Squaric Acid and 2,3-Dimethylpyrazine

A proton-transfer reaction between squaric acid (H 2 sq) and 2,3-dimethylpyrazine (2,3-Me 2 pyz) results in crystallization of a new organic antiferroelectric (AFE), (2,3-Me 2 pyzH + )(Hsq – )·H 2 O ( 1 ), which possesses a layered structure. The structure of each layer can be described as partitioned into strips lined with methyl groups of the Me 2 pyzH + cations and strips featuring extensive hydrogen bonding between the Hsq – anions and water molecules. Variable-temperature dielectric measurements and crystal structures determined through a combination of single-crystal X-ray and neutron diffraction reveal an AFE ordering at 104 K. The phase transition is driven by ordering of protons within the hydrogen-bonded strips. Considering the extent of proton transfer, the paraelectric (PE) state can be formulated as (2,3-Me 2 pyzH + ) 2 (Hsq 2 3– )(H 5 O 2 + ), whereas the AFE phase can be described as (2,3-Me 2 pyzH + )(Hsq – )(H 2 O). The structural transition caused by the localization of protons results in the change in color from yellow in the PE state to colorless in the AFE state. The occurrence and mechanism of the AFE phase transition have been also confirmed by heat capacity measurements and variable-temperature infrared and Raman spectroscopy. This work demonstrates a potentially promising approach to the design of new electrically ordered materials by engineering molecule-based crystal structures in which hydrogen-bonding interactions are intentionally partitioned into quasi-one-dimensional regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits

We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against excitation loss in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate κ 1 and the engineered dissipation rate κ 2 . Under a practical noise ratio κ 1 /κ 2 = 10 -3 , the repetition-SC scheme can reach a 10 -15 logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Validation of a Cephalad Fluid Shift Countermeasure

INTRODUCTION: This project will provide critical data required to objectively determine how an optimized thigh cuff could be incorporated into the NASA integrated physiological countermeasure suite. This project will determine if thigh cuffs used during simulated spaceflight impact intracranial pressure (ICP), ocular structure and function, and intraocular pressure (IOP) using state of-the-art techniques. Additionally, some of the same methods, hardware, and protocols will be employed in the present investigation to enable direct comparisons to the International Space Station (ISS) "Fluid Shifts" experiment with Chibis-Lower Body Negative Pressure (LBNP). This study will determine the temporal physiological responses of thigh cuff application and removal on ocular and cerebral variables (including invasive ICP) in a microgravity analog. Furthermore, this proposed study will determine tissue pressure distribution applied by thigh cuffs in order to improve comfort, mobility, and efficacy of the countermeasure. Our specific aim is to determine the efficacy of a novel thigh cuff device to mitigate cephalad fluid shifts. We hypothesize that a thigh cuff countermeasure employed in a microgravity analog will temporarily reverse or attenuate ocular and cerebral-volume-pressure variables, approaching normal Earth-based seated posture, the most frequent posture assumed in daily life. In addition, we hypothesize that the magnitude of fluid and pressure redistribution using a thigh cuff countermeasure may require a longer exposure time than that of Chibis-LBNP (using ground-based data from our "Fluid Shifts" project). This project directly addresses Critical Path Roadmap Risks and Questions regarding "Risk of Spaceflight-Induced Intracranial Hypertension/Vision Alterations," and IRP Gap VIIP13: We need to identify preventative and treatment countermeasures to mitigate changes in ocular structure and function and intracranial pressure during spaceflight. METHODS: Noninvasive measures and tissue pressure distributions beneath thigh cuffs The objectives of this study are to: 1) determine the distribution of skin surface pressures beneath the advanced thigh cuff in ten subjects, 2) calibrate the built-in pressure measurement system of the advanced thigh cuff using an industry standard device, and 3) collect subjective feedback and data on the new cuff design to allow for further adjustments prior to invasive studies. A Tekscan Industrial Sensing (I-Scan) system will measure the pressure distribution of the advanced thigh cuff against the skin. In addition, we will measure blood pooling in the thigh and record the circumference of the thigh using Hokanson strain gauge plethysmography. The advanced thigh cuff will be adjusted to obtain a skin contact pressure of 30-50 mmHg as visualized on the Tekscan system. The built-in advanced thigh cuff pressure monitor will be recorded simultaneously to allow direct comparison to the Tekscan measurements. The volunteer will then remove the thigh cuff and remain at rest for five minutes with no legging applied. The thigh cuff will be donned again and pressure measurements will be taken in the same manner for up to 10 repetitions to show reproducibility of pressure after donning. At the conclusion of the study, subjects will be asked to flex their knee, stand, walk, and sit with the thigh cuff activated. During each of these maneuvers the subject will rate their pain/comfort using a modified Borg scale. Effect of thigh cuffs on ICP during simulated microgravity Ommaya reservoir patients will be recruited from the John Wayne Cancer Institute. Ommaya reservoirs provide safe and direct access for the measurement of ICP. Subjects will be instrumented for continuous blood pressure, ECG, and invasive ICP measures. The subjects will be positioned in the upright sitting posture for a 10-minute stabilization period. After the 10-minute stabilization period, imaging measures [ICP, Optical Coherence Tomography, IOP, ocular and vascular ultrasound] will be performed. Following baseline seated measures, the subject will be positioned randomly in the supine, 15deg head-down-tilt, and 15deg head-down-tilt with thigh cuffs and measures repeated. DISCUSSION: Tests to down-select thigh cuff designs will occur in early 2016. Invasive ICP and noninvasive eye imaging tests will begin in spring 2016. Supported by NSBRI through NCC 9-58.

Macias, B.↗

Search for transient optical counterparts to high-energy IceCube neutrinos with Pan-STARRS1

In order to identify the sources of the observed diffuse high-energy neutrino flux, it is crucial to discover their electromagnetic counterparts. To increase the sensitivity of detecting counterparts of transient or variable sources by telescopes with a limited field of view, IceCube began releasing alerts for single high-energy ( E ν > 60 TeV) neutrino detections with sky localisation regions of order 1° radius in 2016. We used Pan-STARRS1 to follow-up five of these alerts during 2016–2017 to search for any optical transients that may be related to the neutrinos. Typically 10–20 faint ( m i P1 ≲ 22.5 mag) extragalactic transients are found within the Pan-STARRS1 footprints and are generally consistent with being unrelated field supernovae (SNe) and AGN. We looked for unusual properties of the detected transients, such as temporal coincidence of explosion epoch with the IceCube timestamp, or other peculiar light curve and physical properties. We found only one transient that had properties worthy of a specific follow-up. In the Pan-STARRS1 imaging for IceCube-160427A (probability to be of astrophysical origin of ~50%), we found a SN PS16cgx, located at 10.0' from the nominal IceCube direction. Spectroscopic observations of PS16cgx showed that it was an H-poor SN at redshift z = 0.2895 ± 0.0001. The spectra and light curve resemble some high-energy Type Ic SNe, raising the possibility of a jet driven SN with an explosion epoch temporally coincident with the neutrino detection. However, distinguishing Type Ia and Type Ic SNe at this redshift is notoriously difficult. Based on all available data we conclude that the transient is more likely to be a Type Ia with relatively weak Si II absorption and a fairly normal rest-frame r -band light curve. If, as predicted, there is no high-energy neutrino emission from Type Ia SNe, then PS16cgx must be a random coincidence, and unrelated to the IceCube-160427A. We find no other plausible optical transient for any of the five IceCube events observed down to a 5 σ limiting magnitude of m i P1 ≈ 22 mag, between 1 day and 25 days after detection.

79 ASTRONOMY AND ASTROPHYSICS↗

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗

Field-induced phase coexistence in an artificial spin ice

Artificial spin-ice systems are magnetic metamaterials consisting of nanomagnet arrays that can be designed to study exotic magnetic states not found in natural materials. Typically, these arrays are modelled as interacting binary macrospins that can only be in an up or down state and are described by the Ising model. These materials have demonstrated ordering transitions, but only via a spontaneous symmetry-breaking mechanism. In this study, we have designed and studied a quadrupole artificial spin-ice system consisting of interacting plaquettes of coupled single-domain nanomagnets that can be interpreted as a composite, ternary variable. After annealing this system in an external magnetic field, we observe both a ferroquadrupolar and an antiferroquadrupolar phase, with an apparent first-order phase boundary and a coexistence regime. The phase diagram of this material is reminiscent of a model used to describe phase coexistence in the superfluid transition of 4 He with 3 He impurities. Finally, these results illustrate how composite magnetic objects realize exotic statistical physics models beyond the Ising model.

36 MATERIALS SCIENCE↗