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At least 343 records · Page 19

Nanoscale-correlated octahedral rotations in BaZrO 3

BaZrO 3 is reportedly one of few perovskites that retains an ideal cubic structure down to zero Kelvin even though its ground state as predicted by first-principles calculations has remained contentious. Here, we combine electron diffraction with total neutron scattering measured on ceramic samples at cryogenic temperatures to demonstrate that below 80 K, this compound undergoes a structural change associated with the onset of correlated out-of-phase rotations of [ZrO 6 ] octahedra. Here, the change is manifested in the appearance of weak but relatively sharp superlattice reflections at ½hkl (h, k, l = odd), which are readily detectable by electron diffraction. Atomistic structural refinements from the total neutron scattering data confirmed that these reflections are associated with octahedral tilting. The observed rotations are consistent with the a 0 a 0 c - type and feature a coherence length of about 3 nm. The average structure of BaZrO 3 , as seen by Bragg diffraction, remains cubic. According to the electron diffraction data, Nb-doped BaZrO 3 undergoes a similar structural transition but in this case, the tilting couldn't be recovered from the neutron scattering, suggesting that the distortions are smaller compared to those in the pure compound.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Measurement of Heat of Vaporization for Research Gasolines and Ethanol Blends by DSC/TGA

The heat of vaporization (HOV) is a relatively poorly studied fuel property that can be related to a fuel's evaporation characteristics and knock resistance and, therefore, the emissions and efficiency of direct-injection spark-ignition engines. Methods for measuring the HOV of complex gasoline mixtures and blends of gasoline with ethanol and other oxygenates require additional development. Recently, we described a differential scanning calorimetry/thermogravimetric (DSC/TGA) method to perform HOV measurements. Herein we describe a detailed investigation of factors affecting the precision and accuracy of the DSC/TGA method and examine enthalpy evolution and mass loss rate for research gasolines as a function of fraction evaporated. Examination of n-hexane evaporation using several DSC/TGA pan/lid configurations showed that initial sample loss can be reduced using a well-fitting pinhole lid on the sample pan, which reduces the evaporation rate during the balance of the experiment. However, additional experiments with research gasolines revealed that tight lid placement on the pans is not always achieved. Nevertheless, accurate total HOV measurements, with less than 10% initial sample loss, could be achieved for low volatility gasolines regardless of lid placement. A higher mass loss might be expected for higher vapor pressure (wintertime) gasolines. Because of variations in pan lids and their placement and their significant impact on results, quantitative comparisons between different samples of mass loss rate and heat flow curves versus time or fraction evaporated are not yet possible. However, features in the mass loss rate and heat flow curves are reproducible. Furthermore, results show that ethanol-gasoline blend evaporation is highly influenced by the formation of near-azeotropic mixtures of ethanol and specific gasoline components, causing a flattening of the mass and heat curves, with a sharp evaporation rate reduction after the ethanol is evaporated.

33 ADVANCED PROPULSION SYSTEMS↗

Understanding resonant tunnel transport in non-identical and non-aligned clusters as applied to disordered carbon systems

We study the conductance spectra and the corresponding current-voltage characteristics of a set of three impurity clusters of different sizes arranged in the form of a scalene triangle and compare with the transport of their horizontal and vertical configurations. The tuning capability of resonant tunnelling features in a quantum dot device made of these non-aligned impurity clusters is demonstrated by re-distributing their diameters and inter-cluster distances in a systematic manner. By manipulating the inter-cluster coupling for a scalene triangular configuration, the transition of current-voltage curves from a step-like feature to a negative differential resistance can be produced. This process also yields conductance features for triangular configurations, which can be compared to the quantum dot structures perfectly aligned to the direction of the propagating wavevector. The strength of inter-cluster coupling or order parameter for these configurations is analysed from the relative variation of the width and the energy difference of the sharp and broad peaks observed in the density of states spectra. Based on the relative change of the inter-cluster coupling with the cluster configurations, a transport model applicable to structurally inhomogeneous systems is proposed in order to explain the experimentally observed variation of the energy band gap with the disorder parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Temporal entanglement transitions in the periodically driven Ising chain

Periodically driven quantum systems can host non-equilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover (TET) in a Floquet spin chain, which correspond to a quantum phase transition in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking. We identify the symmetry principles underlying these transitions: they appear when the driven Hamiltonian preserves global symmetry (here, ℤ2), the initial state respects this symmetry, and the reduced density matrix carries weight in both subsystem-parity sectors, with TET occurring precisely when the sector weights become equal (given the previous two conditions are also satisfied). Intriguingly, we find these transitions across a broad range of driving frequencies (from adiabatic to high-frequency regime) and independently of drive details, where they manifest as periodic, sharp entanglement spectrum reorganizations marked by the Schmidt-gap closure, a vanishing entanglement echo, and symmetry-quantum-number flips, while remaining invisible to conventional local observables. At high frequencies, the entanglement Hamiltonian acquires an intrinsic timescale decoupled from the drive period, rendering the transitions genuine steady-state features. Finite-size scaling reveals universal critical behavior with correlation-length exponent 𝜈 = 1, matching equilibrium Ising universality despite its emergence from purely dynamical mechanisms decoupled from static criticality. Furthermore, our work establishes TET as novel features in Floquet quantum matter.

36 MATERIALS SCIENCE↗

SOC Synthetic Microstructure Bank

QUICK START: Start with property_library.html (can be found by typing the filename into the query box) and use the interactive table to filter, sort, and select a microstructure with the desired properties. Search for the alphabetic code to obtain the corresponding dataset. Full description: This is a bank of 1,970 unique 3-phase electrode microstructure files. When you account for reassigning phase IDs (e.g. declare that 1=Ni and 2=pore, instead of 1=pore and 2=Ni), it actually represents 5,910 unique electrode microstructures, each of which could be considered to be either an air or a fuel electrode (e.g. declare that the phase IDs correspond to pore, Ni, and YSZ; or that they correspond to pore, LSCF, and GDC; or whatever electron-conductor and ion-conductor combination is being studied). The voxel size is 50 nm and each electrode file contains a 4x4 grid of (12.5 micron)^3 sub-volumes. If placed together in a grid, they comprise a 50x50x12.5 micron electrode (note that the interfaces between sub-volumes will be sharp; this can be mitigated via simulating annealing/relaxation). The sub-volumes can also be used individually for a reasonably sized 12.5 micron cubic region-of-interest. A user can simply consider the voxel size to be a different value to rescale the volumes (and all of their morphological features, including particle size) as desired. These microstructures were generated using DREAM3D. The general procedure is outlined in https://doi.org/10.1016/j.jpowsour.2018.03.025 The file names are an alphabetic code having to do with the input parameters used in DREAM3D when they were generated. Most users would be best served by starting with the file property_library.html or property_library_subvols.html (which lists properties for each individual subvolume). These files contain a catalogue of the actual, measured properties of every microstructure in the database. Any combination of property values can be filtered and sorted until a desired electrode is found, at which point the user can find the file corresponding to that alphabetic code. The properties in the catalogue include connected TPB density, and for each phase: phase fraction, average particle size, polydispersity of particle size, tortuosity, and connected pair-wise interfacial area. They also include what fraction of each property is connected through to the interfaces of the volume. If the desired combination of properties is not found at first, remember that the phase IDs can be re-assigned arbitrarily, e.g. swapping 1s and 2s. In fact, the database was generated with this in mind so as not to generate redundant microstructures. If the database does not contain the desired property combinations, try to search for the other possible permutations of those properties with re-assigned phase IDs. Please cite https://doi.org/10.1149/10301.0909ecst for use. Please contact the maintainer, William K. Epting, for additional information or assistance.

3D microstructure↗

Origin of structural analogies and differences between the atomic structures of GeSe{sub 4} and GeS{sub 4} glasses: A first principles study

First-principles molecular dynamics simulations based on density functional theory are employed for a comparative study of structural and bonding properties of two stoichiometrically identical chalcogenide glasses, GeSe{sub 4} and GeS{sub 4}. Two periodic cells of 120 and 480 atoms are adopted. Both glasses feature a coexistence of Ge-centered tetrahedra and Se(S) homopolar connections. Results obtained for N = 480 indicate substantial differences at the level of the Se(S) environment, since Ge–Se–Se connections are more frequent than the corresponding Ge–S–S ones. The presence of a more prominent first sharp diffraction peak in the total neutron structure factor of glassy GeS{sub 4} is rationalized in terms of a higher number of large size rings, accounting for extended Ge–Se correlations. Both the electronic density of states and appropriate electronic localization tools provide evidence of a higher ionic character of Ge–S bonds when compared to Ge–Se bonds. An interesting byproduct of these investigations is the occurrence of discernible size effects that affect structural motifs involving next nearest neighbor distances, when 120 or 480 atoms are used.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains

We report on the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading quasiparticles. We derive a generalized hydrodynamic theory for dynamics in such random integrable systems, including diffusive corrections due to disorder, and use it to study nonequilibrium energy and spin transport. We demonstrate that diffusive corrections to the ballistic propagation of quasiparticles can arise even in noninteracting settings, in sharp contrast to clean integrable systems. This suggests that operator fronts broaden diffusively in random integrable systems. By tuning parameters in the disorder distribution, one can drive this model through an unusual phase transition, between a phase where all wave functions are delocalized and a phase in which low-energy wave functions are quasilocalized (in a sense we specify). Both phases have ballistic transport; however, in the quasilocalized phase, local autocorrelation functions decay with an anomalous power law, and the density of states diverges at low energy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic Monopoles and Dark Matter

Schwinger’s idea about the magnetic world of the early Universe, in which magnetic charges (monopoles) and magnetic atoms (g{sup +}g{sup –}) could be formed, is developed. In the present-day Universe magnetic charges with energies in the GeV range can be formed in the magnetospheres of young pulsars in superstrong magnetic fields. Spectroscopic features of magnetic atoms and possibilities for their observations are discussed. Relic magnetic atoms can contribute up to 18% to the dark matter density. The gamma-ray excess at our Galactic center could arise under two-photon annihilation of magnetic charges as a cooperative effect from neutron stars. A sharp physical difference of Schwinger’s magnetic world from Dirac’s present-day electric world is pointed out. Artificial magnetic monopoles are also mentioned briefly.

79 ASTRONOMY AND ASTROPHYSICS↗

Summary of the the 11th Symposium of the International Society of Root Research

11th Symposium of the International Society of Root Research (ISRR11) and the 9th International Symposium on Root Development (Rooting2021) - Root Biology Never Sleeps virtual meeting May 24 - 28. These meetings are generally held in separate years. However, because of travel restrictions imposed by the COVID-19 pandemic, the organizing committees of both symposia decided to host the two meetings as a fully-joint and virtual-only conference. Various time zones were considered when developing the schedule, as live interactions was an important focus. Scientific sessions were held from 3 a.m. to 10 p.m. US Central Daylight Time (CDT) to meet the international demand. More than 700 participants from 52 countries virtually attend both events which featured 74 talks in 16 sessions including: 10 plenary lectures, 16 keynote speakers and 48 selected talks. Additionally, nearly 300 posters were presented in nine poster sessions. The meeting also featured an Ambassador Program with 21 ambassadors from 10 countries. These ambassadors organized a half-day pre-symposium workshop and produced a review of the meeting for “New Phytologist”. The meeting also awarded a Lifetime Award to Dr. Wendy Silk (Prof. Emerita University of California, Davis). Committee Members: • Bob Sharp (Chair) – University of Missouri • Felix Fritschi (Chair, Int’l Program Committee) – University of Missouri • David Braun – University of Missouri • Vicki Bryan – University of Missouri • Rich Ferrieri – University of Missouri • Laura Greeley – University of Missouri (postdoctoral representative) • Ali Housh – University of Missouri (graduate student representative) • Allison Miller – Donald Danforth Plant Science Center and St Louis University • Mel Oliver – University of Missouri • Jonathan Stemmle – University of Missouri • Gus Thies – University of Missouri & Donald Danforth Plant Science Center (graduate student representative) • Chris Topp - Donald Danforth Plant Science Center

Root Biology↗

Electrochemical strain microscopy with blocking electrodes: The role of electromigration and diffusion

Electrochemical strains are a ubiquitous feature of solid state ionic devices ranging from ion batteries and fuel cells to electroresistive and memristive memories. We proposed a scanning probe microscopy (SPM) based approach, referred as electrochemical strain microscopy (ESM), for probing local ionic flows and electrochemical reactions in solids based on bias-strain coupling. In ESM, the sharp SPM tip concentrates the electric field in a small (10-50 nm) region of material, inducing interfacial electrochemical processes and ionic flows. Furthermore, we use the resultant electrochemical strains to determine it from dynamic surface displacement and provide information on local electrochemical functionality. We also analyze image formation mechanism in ESM for a special case of mixed electronic-ionic conductor with blocking tip electrode, and determine frequency dependence of response, role of diffusion and electromigration effects, and resolution and detection limits.

36 MATERIALS SCIENCE↗

Electromagnetic Launcher with Massive Light-Plasma Initiator

The results of experiments with an initiator of lithium and graphite, whose mass was 10% of the mass of the projectile, are presented. Similar initiators produce plasma with a high speed of sound and provide the initial speed of the projectile of ∼0.5 km/s. The droplet-shaped damage on the insulating wall of the accelerator channel are described. The link between the appearance of these damages and the sharp deceleration of the plasma piston (PP) is noted. A hypothesis relating the occurrence of damages to the resonant deformation of the channel under the action of a moving high-pressure front is discussed. It is shown that the hypothesis about the resonant deformation of the channel qualitatively explains the known features of the accelerator operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

WE-G-207-05: Relationship Between CT Image Quality, Segmentation Performance, and Quantitative Image Feature Analysis

Purpose: Segmentation quality can affect quantitative image feature analysis. The objective of this study is to examine the relationship between computed tomography (CT) image quality, segmentation performance, and quantitative image feature analysis. Methods: A total of 90 pathology proven breast lesions in 87 dedicated breast CT images were considered. An iterative image reconstruction (IIR) algorithm was used to obtain CT images with different quality. With different combinations of 4 variables in the algorithm, this study obtained a total of 28 different qualities of CT images. Two imaging tasks/objectives were considered: 1) segmentation and 2) classification of the lesion as benign or malignant. Twenty-three image features were extracted after segmentation using a semi-automated algorithm and 5 of them were selected via a feature selection technique. Logistic regression was trained and tested using leave-one-out-cross-validation and its area under the ROC curve (AUC) was recorded. The standard deviation of a homogeneous portion and the gradient of a parenchymal portion of an example breast were used as an estimate of image noise and sharpness. The DICE coefficient was computed using a radiologist’s drawing on the lesion. Mean DICE and AUC were used as performance metrics for each of the 28 reconstructions. The relationship between segmentation and classification performance under different reconstructions were compared. Distributions (median, 95% confidence interval) of DICE and AUC for each reconstruction were also compared. Results: Moderate correlation (Pearson’s rho = 0.43, p-value = 0.02) between DICE and AUC values was found. However, the variation between DICE and AUC values for each reconstruction increased as the image sharpness increased. There was a combination of IIR parameters that resulted in the best segmentation with the worst classification performance. Conclusion: There are certain images that yield better segmentation or classification performance. The best segmentation Result does not necessarily lead to the best classification Result. This work has been supported in part by grants from the NIH R21-EB015053. R Nishikawa is receives royalties form Hologic, Inc.

60 APPLIED LIFE SCIENCES↗

Enabling high-temperature nanophotonics for energy applications

The nascent field of high-temperature nanophotonics could potentially enable many important solid-state energy conversion applications, such as thermophotovoltaic energy generation, selective solar absorption, and selective emission of light. However, special challenges arise when trying to design nanophotonic materials with precisely tailored optical properties that can operate at high-temperatures (> 1,100 K). These include proper material selection and purity to prevent melting, evaporation, or chemical reactions; severe minimization of any material interfaces to prevent thermomechanical problems such as delamination; robust performance in the presence of surface diffusion; and long-range geometric precision over large areas with severe minimization of very small feature sizes to maintain structural stability. We report an approach for high-temperature nanophotonics that surmounts all of these difficulties. It consists of an analytical and computationally guided design involving high-purity tungsten in a precisely fabricated photonic crystal slab geometry (specifically chosen to eliminate interfaces arising from layer-by-layer fabrication) optimized for high performance and robustness in the presence of roughness, fabrication errors, and surface diffusion. It offers near-ultimate short-wavelength emittance and low, ultra-broadband long-wavelength emittance, along with a sharp cutoff offering 4:1 emittance contrast over 10% wavelength separation. This is achieved via Q-matching, whereby the absorptive and radiative rates of the photonic crystal’s cavity resonances are matched. Strong angular emission selectivity is also observed, with short-wavelength emission suppressed by 50% at 75° compared to normal incidence. Finally, a precise high-temperature measurement technique is developed to confirm that emission at 1,225 K can be primarily confined to wavelengths shorter than the cutoff wavelength.

14 SOLAR ENERGY↗

Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids

Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW{sub 16}). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW{sub 20}), silicon (SW{sub 21}), and water (SW{sub 23.15} or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S{sub trip}, is also studied. S{sub trip} is a good entropy estimator for liquids where pair and triplet correlations are important such as Ge and Si, but loses accuracy for purely pair-dominated liquids, like LJ fluid, or near the crystallization temperature (T{sub thr}). Since local tetrahedral order is compatible with both liquid and crystalline states, the reorganisation of tetrahedral liquids is accompanied by a clear rise in the pair, triplet, and thermodynamic contributions to the heat capacity, resulting in the heat capacity anomaly. In contrast, the pair-dominated liquids show increasing dominance of triplet correlations on approaching crystallization but no sharp rise in either the pair or thermodynamic heat capacities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High‐pressure phases in shock‐induced melt of the unique highly shocked LL 6 chondrite Northwest Africa 757

Abstract Northwest Africa 757 is unique in the LL chondrite group because of its abundant shock‐induced melt and high‐pressure minerals. Olivine fragments entrained in the melt transform partially and completely into ringwoodite. Plagioclase and Ca‐phosphate transform to maskelynite, lingunite, and tuite. Two distinct shock‐melt crystallization assemblages were studied by FIB ‐ TEM analysis. The first melt assemblage, which includes majoritic garnet, ringwoodite plus magnetite‐magnesiowüstite, crystallized at pressures of 20–25 GP a. The other melt assemblage, which consists of clinopyroxene and wadsleyite, solidified at ~15 GP a, suggesting a second veining event under lower pressure conditions. These shock features are similar to those in S6 L chondrites and indicate that NWA 757 experienced an intense impact event, comparable to the impact event that disrupted the L chondrite parent body at 470 Ma.

Hu, Jinping↗

Resonant Two-Photon Photoelectron Imaging and Intersystem Crossing from Excited Dipole-Bound States of Cold Anions

In this work, we report the observation of a dipole-bound state (DBS) 659 cm –1 below the electron detachment threshold of cryogenically cooled deprotonated 4,4'-biphenol anion (bPh – ) and 19 of its lowest vibrational levels. Resonant two-photon photoelectron imaging (R2P-PEI) via the vibrational levels of the DBS displays a sharp peak with a constant binding energy. This observation indicates vertical detachment from the vibrational levels of the DBS to the corresponding neutral levels with the conservation of the vibrational energy, suggesting that the highly diffuse electron in the DBS has little effect on the neutral core. The R2P-PEI spectra also exhibit two features at lower binding energies, which come from intersystem crossings from the DBS to two lower-lying valence-bound triplet excited states of bPh – . The current study discloses the first R2P-PEI spectra from vibrational excited states of a DBS and direct spectroscopic evidence of transitions from a DBS to valence-bound states of anions.irect spectroscopic evidence of transitions from a DBS to valence-bound states of anions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Harnessing the Spin-Flip Radiative Lifetimes of Optically Addressable Molecular Qubits

Optically addressable molecular qubits based on spin-flip (SF) emissive transitions are promising candidates for quantum technologies due to their sharp luminescence lines and tunable optical-spin interfaces. Yet, the microscopic mechanisms controlling the spin-flip radiative lifetime of SF emitters, a key property for efficient spin readout, remain largely unexplored. Here, we present a computational study of several Cr 4+ and Mo 4+ pseudotetrahedral molecular qubits, and we identify chemical and structural features that influence the transition dipole moment associated with the SF emission, which, in turn, governs the SF radiative lifetime. We find that the magnitude of the dipole moment is governed by the multireference character of the spin-flip excited-state wave function, which can be modulated by tuning the energy separation between the d orbitals of the metal and the spin-pairing energy. Both parameters are sensitive to molecular symmetry, metal–ligand bond covalency, and bond anisotropy and leave room for modulation via ligand and metal design, as well as applied strain, which is relevant for sensing applications. Our findings provide a mechanistic framework for understanding and tuning the spin-flip radiative behavior of molecular qubits and SF emitters that may guide future advances in quantum information science.

molecular qubits↗

Strong Stability Preserving Integrating Factor Two-Step Runge-Kutta Methods

In this report, problems with components that feature significantly different time scales, where the stiff time-step restriction comes from a linear component, implicit-explicit (IMEX) methods alleviate this restriction if the concern is linear stability. However, when nonlinear non-inner-product stability properties are of interest, such as in the evolution of hyperbolic partial differential equations with shocks or sharp gradients, linear inner-product stability is no longer sufficient for convergence, and so strong stability preserving (SSP) methods are often needed. Where the SSP property is needed, IMEX SSP Runge-Kutta (SSP-IMEX) methods have very restrictive time-steps. An alternative to SSP-IMEX schemes is to adopt an integrating factor approach to handle the linear component exactly and step the transformed problem forward using some time-evolution method. The strong stability properties of integrating factor Runge-Kutta methods were established in Isherwood et al. (SIAM J Numer Anal 56(6):3276–3307, 2018), where it was shown that it is possible to define explicit integrating factor Runge-Kutta methods that preserve strong stability properties satisfied by each of the two components when coupled with forward Euler time-stepping. It was proved that the solution will be SSP if the transformed problem is stepped forward with an explicit SSP Runge-Kutta method that has non-decreasing abscissas. However, explicit SSP Runge-Kutta methods have an order barrier of p=4, and sometimes higher order is desired. In this work we consider explicit SSP two-step Runge-Kutta integrating factor methods to raise the order. We show that strong stability is ensured if the two-step Runge-Kutta method used to evolve the transformed problem is SSP and has non-decreasing abscissas. We find such methods up to eighth order and present their SSP coefficients. Adding a step allows us to break the fourth order barrier on explicit SSP Runge-Kutta methods; furthermore, our explicit SSP two-step Runge-Kutta methods with non-decreasing abscissas typically have larger SSP coefficients than the corresponding one-step methods. A selection of our methods are tested for convergence and demonstrate the design order. We also show, for selected methods, that the SSP time-step predicted by the theory is a lower bound of the allowable time-step for linear and nonlinear problems that satisfy the total variation diminishing (TVD) condition. We compare some of the non-decreasing abscissa SSP two-step Runge-Kutta methods to previously found methods that do not satisfy this criterion on linear and nonlinear TVD test cases to show that this non-decreasing abscissa condition is indeed necessary in practice as well as theory. We also compare these results to our SSP integrating factor Runge-Kutta methods designed in Isherwood et al. (2018).

97 MATHEMATICS AND COMPUTING↗