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The radial phase variation of reversed-shear and toroidicity-induced Alfvén eigenmodes in DIII-D
The eigenfunction of an instability contains information about energy flow in the wave. Here, the amplitude and phase of electron cyclotron emission radiometer data from hundreds of DIII-D reversed shear Alfvén eigenmodes (RSAE) and toroidicity-induced Alfvén eigenmodes (TAE) are analyzed along the outboard horizontal midplane. The radial phase profile can be flat, linearly rising or falling, convex or concave; in other words, a wide variety of shapes is observed. For a particular mode, often the radial phase profile remains approximately constant as the mode evolves in time but sometimes it changes rapidly. Many TAEs and some RSAEs have phase profiles that are rather flat where the mode amplitude is largest but rise steadily by ~2π at large major radius. Rapid phase changes are observed when the frequencies of an RSAE and TAE overlap and the modes couple. The phase profile depends weakly on the fast-ion gradient that would appear in the absence of wave-induced transport. Linear and quadratic fits to the phase profiles, together with many plasma parameters, are assembled into RSAE and TAE databases. In both cases, large variability is observed. For RSAEs, the strongest phase dependencies are on electron temperature T e , RSAE mode frequency, and the density of carbon impurities. For TAEs, the strongest dependencies are on beam power and major radius of the mode. In general, the average RSAE radial phase profile is essentially flat but the TAE profile has non-zero slope and curvature.
Atomic-Scale Mapping and Quantification of Local Ruddlesden–Popper Phase Variations
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A variational phase-field framework for thermal softening and dynamic ductile fracture
A variational phase field model for dynamic ductile fracture is presented. Here, the model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence function to degrade fracture energy during regimes of high plastic flow. A variationally consistent form of the Johnson–Cook model is developed for use with the framework. Results from various benchmark problems in dynamic ductile fracture are presented to demonstrate capabilities. In particular, the ability of the model to regularize shear band formation and subsequent damage evolution in two- and three-dimensional problems is demonstrated. Importantly, these phenomena are naturally captured through the underlying physics without the need for phenomenological criteria such as stability thresholds for the onset of shear band formation.
Impact of longitudinal phase-matching variations on three-wave nonlinear interactions
A general study of three-wave nonlinear mixing in the presence of longitudinal variations in phase-matching conditions is presented. The efficiency of second-harmonic generation and optical parametric amplification is quantified using a normalized set of equations and a polynomial description of the wave-vector mismatch as a function of the longitudinal coordinate. These modeling results are used to estimate the impact of spatial variations in wave-vector mismatch experimentally obtained for five partially deuterated potassium dihydrogen phosphate crystals. The longitudinal inhomogeneities in the properties of crystals of similar quality are not expected to have a significant impact on their use for second-harmonic generation and optical parametric amplification, but the efficiency of nonlinear processes in crystals with larger variations could decrease.
Elastic Bayesian Model Calibration
Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have resulted in tools for emulation, sensitivity analysis, and calibration that are widely used. However, many of these tools do not perform well when the computer model’s parameters control both the amplitude variation of the functional output and its alignment (or phase variation). This paper introduces a framework for Bayesian model calibration when the model responses are misaligned functional data. The approach generates two types of data out of the misaligned functional responses: (1) aligned functions so that the amplitude variation is isolated and (2) warping functions that isolate the phase variation. These two types of data are created for the computer simulation data (both of which may be emulated) and the experimental data. The calibration approach uses both types so that it seeks to match both the amplitude and phase of the experimental data. The framework is careful to respect constraints that arise, especially when modeling phase variation, and is framed in a way that it can be done with readily available calibration software. In conclusion, we demonstrate the techniques on two simulated data examples and on two dynamic material science problems: a strength model calibration using flyer plate experiments and an equation of state model calibration using experiments performed on the Sandia National Laboratories’ Z-machine.
Phase Modeling of the TRAPPIST-1 Planetary Atmospheres
Transiting compact multiplanet systems provide many unique opportunities to characterize the planets, including studies of size distributions, mean densities, orbital dynamics, and atmospheric compositions. The relatively short orbital periods in these systems ensure that events requiring specific orbital locations of the planets (such as primary transit and secondary eclipse points) occur with high frequency. The orbital motion and associated phase variations of the planets provide a means to constrain the atmospheric compositions through measurement of their albedos. Here we describe the expected phase variations of the TRAPPIST-1 system and times of superior conjunction when the summation of phase effects produce maximum amplitudes. We also describe the infrared flux emitted by the TRAPPIST-1 planets and the influence on the overall phase amplitudes. We further present the results from using the global circulation model ROCKE-3D to model the atmospheres of TRAPPIST-1e and TRAPPIST-1f assuming modern Earth and Archean atmospheric compositions. These simulations are used to calculate predicted phase curves for both reflected light and thermal emission components. We discuss the detectability of these signatures and the future prospects for similar studies of phase variations for relatively faint M stars.
Dephasingless two-color terahertz generation
A laser pulse composed of a fundamental and an appropriately phased second harmonic can drive a time-dependent current of photoionized electrons that generates broadband THz radiation. Over the propagation distances relevant to many experiments, dispersion causes the relative phase between the harmonics to evolve. This “dephasing” slows the accumulation of THz energy and results in a multi-cycle THz pulse with significant angular dispersion. Here, we introduce a novel optical configuration that compensates the relative phase evolution, allowing for the formation of a half-cycle THz pulse with almost no angular dispersion. The configuration uses the spherical aberration of an axilens to map a prescribed radial phase variation in the near field to a desired longitudinal phase variation in the far field. Simulations that combine this configuration with an ultrashort flying focus demonstrate the formation of a half-cycle THz pulse with a controlled emission angle and 1/4 the angular divergence of the multi-cycle pulse created by a conventional optical configuration.
Imaging the Phase Transformation in Single Particles of Lithium Titanate Anode for Lithium-ion Batteries
Lithium uptake and release in lithium titanate (LTO) anode materials during a discharge and charge cycle is one of the fundamental processes of a Lithium-ion battery (LIB), still not fully understood at the microscopic level.During discharge cycle, LTO undergoes a phase transformation between Li 4 Ti 5 O 12 and Li 7 Ti 5 O 12 states within a cubic crystal lattice. To reveal the details of the microscopic mechanism,it is necessary to track the sequence of phase transformation sat different discharge/charge states under operating conditions.Here we use in-situ Bragg Coherent Diffraction Imaging (BCDI) and in-situ X-ray diffraction (XRD) experiments to examine the lithium insertion-induced materials phase transformation within a single LTO particle anda bulk battery analogue,respectively. BCDI analysis from (111) Bragg peak, shows the two-phase transformation manifesting as a distinct image phase modulation within a single LTO nanoparticle occurring in the middle of the discharge region then subsiding towards the end of the discharge cycle. We observe the biggest phase variation at the two-phase stage,indicating the formation of phase domains of 200 nm in size during the discharge process. Additionally, we also observe a lattice contraction of >0.2% in a single LTO nanoparticle at the (400) Bragg peak measurement, larger than that in the corresponding bulk material. Our observation of this phase transformation at a single particle level has implications for the understanding of the microscopic/mesoscale picture of the phase transformation in anode and cathode LIBs materials.
Attosecond time delays at Cooper minima in valence-shell photoionization of alkali-metal and alkaline-earth-metal atoms
Ji et al. [New J. Phys. 26, 093014 (2024)] established a direct link between the photoionization cross section and the attosecond time delay near Cooper minima (CM) in the valence shells of noble-gas atoms. This link is based on the analytic properties of the ionization amplitude in the complex plane of the photoelectron energy, and is particularly sensitive to the winding number of the amplitude around the origin of the complex energy plane. Here, in this study, we demonstrate an analogous relation for photoionization of the valence 𝑛𝑠 shells of alkali-metal atoms (AMA), from Na (𝑛 = 3) to Cs (𝑛 = 6), as well as alkaline-earth-metal atoms (AEMA), from Mg (𝑛 = 3) to Ba (𝑛 = 6). To this end, we employ a fully relativistic formalism that separates the two complementary 𝑛𝑠 1/2 → 𝐸𝑝 1/2 and 𝐸𝑝 3/2 ionization channels. Each of these channels exhibits a phase variation close to 𝜋, but in opposite directions, near their respective Cooper minima. This phase variation vanishes in a nonrelativistic formulation, where the two channels become degenerate. For AMA, due to the threshold proximity of the CM, the universal Coulomb contribution to the time delay must be subtracted. The remaining component of the time delay is target-specific, angular-dependent, and accessible through comparative measurements.
A variational phase-field model For ductile fracture with coalescence dissipation
A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling mechanism between plasticity and fracture by degrading the fracture toughness as the equivalent plastic strain increases. The proposed model is compared with a recent alternative where plasticity and fracture are strongly coupled. Several representative numerical examples motivate specific modeling choices. In particular, a linear crack geometric function provides an “unperturbed” ductile response prior to crack initiation, and Lorentz-type degradation functions ensure that the critical fracture strength remains independent of the phase-field regularization length. In addition, the response of the model is demonstrated to converge with a vanishing phase-field regularization length. Additionally, the model is then applied to calibrate and simulate a three-point bending experiment of an aluminum alloy specimen with a complex geometry. The effect of the proposed coalescence dissipation coupling on simulations of the experiment is first investigated in a two-dimensional plane strain setting. The calibrated model is then applied to a three-dimensional calculation, where the calculated load-deflection curves and the crack trajectory show excellent agreement with experimental observations. Finally, the model is applied to simulate crack nucleation and growth in a specimen from a recent Sandia Fracture Challenge.
Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems
Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al. in J Comput Neurosci 38(1):25–51, 2015; Lyttle et al. in Biol Cybern 111(1):25–47, 2017). We established in (Wang et al. in SIAM J Appl Dyn Syst 20(2):701–744, 2021. https://doi.org/10.1137/20M1344974) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates’ hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties.
Dynamics of phage-host interactions in Bacteroides fragilis resolved by single-cell transcriptomics
The interactions between lytic phages and their hosts are typically studied in bulk culture, which obscures cell-cell differences in infection susceptibility or expression of protective factors. Here, we use bacterial single-cell RNA sequencing to profile the transcriptomes of ~50,000 cells from cultures of a human pathobiont, Bacteroides fragilis, infected with a lytic bacteriophage. From a single sampling, we quantified the asynchronous progression of phage infection in individual bacterial cells and reconstructed the infection timeline, characterizing both host and phage transcriptomic changes as infection unfolded. Further, we discovered phenotypic subpopulations of bacteria that remained uninfected. Each cell’s vulnerability to phage infection was influenced by expression of multiple genetic loci, most prominently phase-variable capsular polysaccharide (CPS) biosynthesis pathways and an operon predicted to encode fimbrial genes. These findings uncovered genome-wide phase variation and stochasticity that enable bacterial survival and re-growth without acquiring additional mutations. Overall, we establish bacterial single-cell RNA sequencing as a powerful platform for investigating the dynamics of host-phage interactions and revealing the roles of phase variation and stochasticity in bacterial defenses.
Unbinned extraction of $γ$ from $B\to DK$ with normalizing flows
We introduce an unbinned method for extracting the CKM angle $γ$ from the decay chain $B^\pm \to (D \to K_S π^+ π^-) K^\pm$ using normalizing flows (NFs). The NFs, trained on $D$ decay data, learn a faithful continuous representation of the amplitude and strong phase variation over the $D\to K_Sπ^+π^-$ Dalitz plot whose fidelity improves with increased data sample sizes. With this input, the $B$ decay data can be used to extract the parameters $r_B$, $δ_B$, and $γ$. We test the method on Monte Carlo generated data, where it successfully recovers the injected value of $γ$ within uncertainties. The present implementation propagates statistical uncertainties from finite training data via an ensemble of independently trained flows, and does not attempt to capture the effects of systematic experimental errors. We explore two versions of the method that differ in how the trigonometric constraint on phase variation is encoded, and comment on the possible extension to Bayesian NFs, which would provide direct uncertainty estimates on the learned densities without requiring ensemble training.
Variational Optical Phase Learning on a Continuous-Variable Quantum Compiler
Quantum process learning is a fundamental primitive that draws inspiration from machine learning with the goal of better studying the dynamics of quantum systems. One approach to quantum process learning is quantum compilation, whereby an analog quantum operation is digitized by compiling it into a series of basic gates. While there has been significant focus on quantum compiling for discrete-variable systems, the continuous-variable (CV) framework has received comparatively less attention. We present an experimental implementation of a CV quantum compiler that uses two-mode squeezed light to learn a Gaussian unitary operation. We demonstrate the compiler by learning a parameterized linear phase unitary through the use of target and control phase unitaries to demonstrate a factor of 5.4 increase in the precision of the phase estimation and a 3.6-fold acceleration in the time-to-solution metric when leveraging quantum resources. We further show how our approach can be extended to higher-dimensional compilation tasks. Our results are enabled by the tunable control of our cost landscape via variable squeezing, thus providing a critical framework to simultaneously increase precision and reduce time-to-solution.
Elastic functional changepoint detection of climate impacts from localized sources
Detecting changepoints in functional data has become an important problem as interest in monitoring of climate phenomenon has increased, where the data is functional in nature. Here, the observed data often contains both amplitude (y-axis) and phase (x-axis) variability. If not accounted for properly, true changepoints may be undetected, and the estimated underlying mean change functions will be incorrect. In this article, an elastic functional changepoint method is developed which properly accounts for these types of variability. The method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly or can be computed via functional principal component analysis to ease the computational burden. We apply the method and its nonelastic competitors to both simulated data and observed data to show its efficiency in handling data with phase variation with both amplitude and phase changepoints. We use the method to evaluate potential changes in stratospheric temperature due to the eruption of Mt. Pinatubo in the Philippines in June 1991. Using an epidemic changepoint model, we find evidence of a increase in stratospheric temperature during a period that contains the immediate aftermath of Mt. Pinatubo, with most detected changepoints occurring in the tropics as expected.
The TESS Phase Curve of KELT-1b Suggests a High Dayside Albedo
We measured the optical phase curve of the transiting brown dwarf KELT-1b (TOI 1476) using data from the TESS spacecraft. We found that KELT-1b shows significant phase variation in the TESS bandpass, with a relatively large phase amplitude of 234{sub −44}{sup +43} ppm and a secondary eclipse depth of 371{sub −49}{sup +47} ppm. We also measured a marginal eastward offset in the dayside hot spot of 18.°3 ± 7.°4 relative to the substellar point. We detected a strong phase-curve signal attributed to ellipsoidal distortion of the host star with an amplitude of 399 ± 19 ppm. Our results are roughly consistent with the Spitzer phase curves of KELT-1b, but the TESS eclipse depth is deeper than expected. Our cloud-free 1D models of KELT-1b’s dayside emission are unable to fit the full combined eclipse spectrum. Instead, the large TESS eclipse depth suggests that KELT-1b may have a significant dayside geometric albedo of A {sub g} ∼ 0.5 in the TESS bandpass, which would agree with the tentative trend between equilibrium temperature and geometric albedo recently suggested by Wong et al. We posit that if KELT-1b has a high dayside albedo, it is likely due to silicate clouds that form on KELT-1b’s nightside and are subsequently transported onto the western side of KELT-1b’s dayside hemisphere before breaking up.