Automated Model Selection with First-order Gauge-Invariant Parameters
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Seritan, Stefan Kelley↗
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First Order Transport of a Cold Uniform Ellipsoid of Charge
A single particle has a 6-element phase space vector $s = (x, γv)$ where $γv =\frac{p}{m}$ s proportional to the relativistic momentum. The ellipsoid is represented by a 21-element vector $(s, C, V)$ where $s$ is the phase space location of the centroid. $C$ is the 3 × 3 covariance matrix defined by $C_{ij} = ⟨δx_iδx_j⟩$, where $δx$ is the distance of a particle from the centroid $x$. $C$ is symmetric so only counts as 6 elements of the overall vector. $V$ is a general 3 × 3 matrix that determines the velocity distribution in the bunch by $δ(γv) = Vδx$. In total this makes 6 + 6 + 9 = 21 elements.
43 PARTICLE ACCELERATORS↗
First-Order Phase Transitions in Hyper Stealth Dark Matter
Stealth Dark Matter (SDM) is a theory of composite dark matter where the lightest neutral baryon is the dark matter candidate and other dark hadrons decay in the early universe via suppressed Standard Model interactions. Such dark matter candidates must be heavier than about 500 GeV due to limits set by the LHC. Hyper Stealth Dark Matter (HSDM) is recently described variant where the dark matter candidate can be a baryon as light as 5 GeV and the composite dynamics is similar to one-flavor QCD.
Fleming, George T. [Fermilab] (ORCID:0000000249877↗
Stability of the first-order character of phase transition in HoCo2
Supplementary material for the details of the specific heat and magnetization data.
Kumar, Ajay↗
An asymptotic Grad–Shafranov equation for quasisymmetric stellarators
A first-order model is derived for quasisymmetric stellarators where the vacuum field due to coils is dominant, but plasma-current-induced terms are not negligible and can contribute to magnetic differential equations, with $\beta$ of the order of the ratio induced to vacuum fields. Under these assumptions, it is proven that the aspect ratio must be large and a simple expression can be obtained for the lowest-order vacuum field. The first-order correction, which involves both vacuum and current-driven fields, is governed by a Grad–Shafranov equation and the requirement that flux surfaces exist. These two equations are not always consistent, and so this model is generally overconstrained, but special solutions exist that satisfy both equations simultaneously. One family of such solutions is the set of first-order near-axis solutions. Thus, the first-order near-axis model is a subset of the model presented here. Several other solutions outside the scope of the near-axis model are also found. A case study comparing one such solution to a VMEC-generated solution shows good agreement.
Nikulsin, Nikita (ORCID:0000000318611777)↗
Formation of short-range magnetic order and avoided ferromagnetic quantum criticality in pressurized LaCrGe 3
LaCrGe 3 has attracted attention as a paradigm example of the avoidance of ferromagnetic (FM) quantum criticality in an itinerant magnet. In this work, we combined thermodynamic (specific heat and thermal expansion), transport, x-ray, and neutron scattering as well as μSR measurements to obtain insights on the temperature-pressure phase diagram of LaCrGe 3 . Consistent with previous studies of the phase diagram by transport measurements, our thermodynamic data shows clearly that the FM transition at T FM changes its character from second order to first order when it is suppressed to low temperatures by pressure. In addition, previous studies demonstrated that for high pressures a new phase occurs below T 2 , which was proposed to be a long-wavelength antiferromagnetic state (AFM q ). In this paper, we provide evidence from our thermodynamic data that this phase transition is preceded by yet another phase transition at T 1 >T 2 . Our μSR data indicate that full magnetic volume fraction is only established below T 2 , but that this magnetism is characterized by a short correlation length. Within the experimental resolution, our neutron-scattering data is not able to identify any magnetic Bragg peaks. Overall, the microscopic magnetic data is therefore consistent with the formation of FM clusters in the proximity of the avoided FM quantum critical point in LaCrGe 3 . This conclusion is at odds with the previous proposal of AFM q order and raises questions on the role of disorder in this stochiometric compound.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Loading direction dependence of asymmetric response of pyramidal slip in rolled AZ31 magnesium alloy
Textured magnesium alloys usually exhibit anisotropic mechanical behavior due to the asymmetric activation of different twinning and slipping modes. This work focuses on the pyramidal slip responses of rolled AZ31 magnesium alloy under two loading conditions, compressive and tensile loading along the normal direction. Under the condition where the compressive loading direction is closely parallel to the c-axis of the unit cell, tensile twinning and basal slips are prohibited, dislocations then active and tend to accumulate at grain boundaries and form dislocation walls. Meanwhile, these dislocations exhibit zigzag morphologies, which result from the cross-slip from {$10\bar{1}1$} first-order pyramidal plane to {$11\bar{2}2$} second-order pyramidal plane, then back to {$10\bar{1}1$} first-order pyramidal plane. Under the condition where tensile twins are prevalent, {$10\bar{1}1$} first-order and {$11\bar{2}2$} second-order pyramidal dislocations are favorable to be activated. Both types of dislocations behave climb-like dissociations onto the basal plane, forming zigzag dislocations. first-order pyramidal plane to second-order pyramidal plane, then back to first-order pyramidal plane. Under the condition where tensile twins are prevalent, first-order and second-order pyramidal dislocations are favorable to be activated. Both types of dislocations behave climb-like dissociations onto the basal plane, forming zigzag dislocations.
36 MATERIALS SCIENCE↗
The influence of Au substitution and hydrostatic pressure on the phase transitions and magnetocaloric properties of MnCoGe alloys
In this work, the phase transitions and magnetocaloric properties of Mn 1--x Au x CoGe (0≤x≤0.025) alloys were studied as a function of concentration x and applied hydrostatic pressure. The increasing substitution of Au for Mn results in the decrease of the first-order martensitic transition temperature, and this first-order martensitic transition was ultimately converted to a second-order magnetic transition when the Au substitution (x) reached 0.025. The magnitudes of the maximum magnetic entropy changes increased when the magnetic and structural transitions were coupled, which occurred for 0.005≤x≤0.020. The largest maximum magnetic entropy change for a field change of μ 0 ΔH=7 T was 33.1J/kgK for the sample with x=0.020. Similar to the effect of Au substitution, the first-order martensitic transition temperature initially decreased, and then converted to second order, when the applied hydrostatic pressure reached a large enough value. Interestingly, both Au substitution and pressure application cause a volume reduction and, in both cases, the first-order martensitic transition temperature initially reduced and then converted to second-order. These results suggest two different methods of tuning the transition temperatures in these magnetocaloric materials. One can either apply hydrostatic pressure and temporarily adjust the transition temperatures or modify the composition chemically and permanently change the transition temperatures.
36 MATERIALS SCIENCE↗
Process Interactions Can Change Process Ranking in a Coupled Complex System Under Process Model and Parametric Uncertainty
For a complex hydrologic system with multiple processes and process interactions, global sensitivity analysis is often used to identify important or influential parameters for model development and improvement. The identification is complicated by process model uncertainty, when a system process can be represented by multiple process models. This study develops a new total-effect process sensitivity index to identify influential processes under model uncertainty. This is done by extending Sobol's total-effect parameter sensitivity index for one system model to total-effect process sensitivity index for multiple system models to account for uncertainty in process models and model parameters. The total-effect process sensitivity index includes not only the first-order process sensitivity index for measuring the importance of individual processes but also higher-order indices that account for process interactions. The total-effect process sensitivity index can identify an influential process that itself and its interactions with other processes influence a model output. Here, the total-effect process sensitivity index is applied to two numerical examples: (a) Sobol's G*-functions with analytical solutions of first-order and total-effect process sensitivity indices, and (b) groundwater flow models with interactions between recharge, geology, and snowmelt processes. The second evaluation shows that, due to second-order and higher-order process interactions, the first-order and total-effect process sensitivity indices give different process ranking. It is thus necessary to estimate both first-order and total-effect process sensitivity indices to appreciate the difference between the first-order impact of a process alone and the overall total-effect impact of the process itself and its interactions with other processes on a model output.
54 ENVIRONMENTAL SCIENCES↗
A second-order distributed memory parallel fast sweeping method for the Eikonal equation
The Eikonal equation is used to calculate wave propagation and distance fields, and due to its complexity requires numerical treatment for its solution. In this work, we present a second-order distributed memory parallel fast sweeping method. The second-order solution switches on a two-point stencil when two upwind points are available, and reverts to first-order otherwise. In all examples, the second-order method improves the solution over the first-order, allowing for significant savings in memory while achieving the same accuracy. Parallelization over distributed memory saw good weak scaling with optimal convergence. The computational time for second-order was approximately 2.5 times slower than first-order, where the largest amount of mesh points ran on 144 cores (512 GB) was ≈20 billion. The savings in memory from the second-order method combined with the distributed memory algorithm result in the ability to solve problems much larger than are possible with the serial first-order method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Models for Single–Site Heterogeneous Catalysts on Carbon: MoO 2 Epoxidation Catalyst Anchored to a Fullerene
Single-site molybdenum dioxo catalysts, fullerenol/MoO 2 , are prepared via grafting precursor (DME)MoO 2 Cl 2 onto a highly polyhydroxylated fullerene (ful) and an isomerically-pure and well-defined fullerene (ful*). These catalyst structures are characterized by ICP-OES, XPS, XANES, EXAFS, DRIFT, Raman, and NMR spectroscopy, and DFT. Mo 3d 5/2 XPS and Mo K-edge XANES assign the oxidation state as Mo(VI). Mo EXAFS data fitting reveals two Mo=O double and two Mo–O single bonds at distances of 1.7 and 1.9 Å, respectively, while an Mo=O stretchingl mode is observed at ~950 cm –1 by DRIFT and Raman spectroscopy. These data align well with DFT computational results, supporting the proposed catalyst structure as Fullerene(-μ-O-) 2 M(=O) 2 . Additionally, DFT provides insight into the energetically favorable grafting sites for an isomerically pure fullerenol. The scope of fullerenol/MoO 2 mediated alkene epoxidation includes abiotic alkenes, natural occurring terpenes, and conjugated olefins. For cyclooctene the rate law is first-order in [Mo], near first order in [olefin] and zero-order in [t-butyl hydroperoxide]. A plausible reaction mechanism involves peroxide addition first and then cyclooctene addition directly across the peroxo bond forming the epoxide product, consistent with DFT computation. Overall, fullerenol/MoO 2 shows promise as a sustainable and structurally well-defined system with versatile catalytic activity and good epoxidation recyclability.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Sensitivity Coefficients Calculated for the Prompt Neutron Decay Constant at or Near Delayed Critical [Abstract]
Experimenters at Los Alamos National Laboratory (LANL) measure the prompt neutron decay constant for many experiments at the National Criticality Experiments Research Center (NCERC) to infer reactivity and the effective neutron multiplication factor. These quantities are very important for nuclear criticality safety and validating nuclear data. Uncertainty in measures of criticality of an experimental configuration can be determined prior to physically performing the experiment by applying first order perturbation theory to Monte Carlo codes, such as MCNP®. The first order perturbation theory produces first derivatives of some nuclear parameter to nuclear data (e.g., cross section data). This first derivative is commonly referred to as a sensitivity coefficient. Currently, the MCNP® software has the capability of computing effective neutron multiplication factor sensitivity coefficients to cross section data. This work builds off of this MCNP® capability and the first order perturbation theory to provide a method of calculating sensitivity coefficients for the prompt neutron decay constant at or near delayed critical to cross section data. The prompt neutron decay constant sensitivity coefficient calculated in this work does not depend on any modification of the MCNP® source code. Prompt neutron decay constant sensitivity coefficient calculations can be used to infer reactivity and effective neutron multiplication factor sensitivity coefficient values as well. By investigating the trends of prompt neutron decay constant sensitivity coefficients for nuclide-reaction pairs across energy spectra, experiments can be designed to maximize or minimize the uncertainty in the prompt neutron decay constant in a particular energy region, which can lead to further optimization studies. Prompt neutron decay constant sensitivity coefficients will be calculated for the Jezebel benchmark. Subsequently, these sensitivity coefficients will be used in a data assimilation process to determine if there is or are optimal experiments that can be performed to provide insight into adjustments of uncertain/inaccurate cross section data. Specifically, the effect of the prompt neutron decay constant sensitivity coefficients on the nuclear data-induced uncertainty in the effective neutron multiplication factor will be examined
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Theory of criticality for quantum ferroelectric metals
A variety of compounds, for example, doped paraelectrics and polar metals, exhibit both ferroelectricity and correlated electronic phenomena such as low-density superconductivity and anomalous transport. Characterizing such properties is tied to understanding the quantum dynamics of inversion symmetry breaking in the presence of itinerant electrons. Here, we present a comprehensive analysis of the properties of a metal near a quantum critical transition to a ferroelectric state, in both two and three dimensions. In this study, starting from a minimal model of electrons coupled to a transverse polar phonon via a Rashba-type spin-orbit interaction, we compute the dynamical response of both electrons and phonons. We find that the system can evince both Fermi and non-Fermi liquid phases, as well as enhanced pairing in both singlet and triplet channels. Furthermore, we systematically compute corrections to one-loop theory and find a tendency to quantum order-by-disorder, leading to a phase diagram that can include second-order, first-order, and finite-momentum phase transitions. Finally, we show that the entire phase diagram can be controlled via application of external strain, either compressive or volume-preserving. Our results provide a map of the dynamical and thermodynamical phase space of quantum ferroelectic metals, which can serve in characterizing existing materials and in seeking applications for quantum technologies.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Kinklike structures in an arcsin real scalar dynamics
Highlights: • Kinklike analyses in a real scalar theory with an arcsin dynamic. • First-order formalism implementation and deformation procedure in an arcsin scalar dynamics. In this paper, we analyze kink-like analytical solutions in a real scalar theory with an arcsin dynamics inspired by the arcsin electrodynamics presented in Kruglov (2015). This analysis is done by means of the first-order formalism. This formalism provides a framework where the equations of motion can be simplified by preserving the linear stability of the theory. In this work, the deformation procedure is implemented with the aim of finding exact solutions in systems with generalized dynamics. Along the paper, we explore how the first-order formalism is implemented in the arcsin kinetics and how such a term influences the kink-like solutions. As a part of the result of our paper, we show that the kink-like solutions are similar to the ones obtained in the standard scalar kinetic theory. We also show that the extra parameter, that controls the non-linearities of the model, plays an essential role in the energy densities and stability potentials. These quantities vary according to this parameter. The goals here are to show how the first-order framework is implemented in this arcsin scenario and to present the analytical kink-like solutions that can be found by means of the first-order framework and deformation method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Magnetic Field Reconstruction for a Realistic Multi-Point, Multi-Scale Spacecraft Observatory
Future in situ space plasma investigations will likely involve spatially distributed observatories comprised of multiple spacecraft, beyond the four and five spacecraft configurations currently in operation. Inferring the magnetic field structure across the observatory, and not simply at the observation points, is a necessary step towards characterizing fundamental plasma processes using these unique multi-point, multi-scale data sets. We propose improvements upon the classic first-order reconstruction method, as well as a second-order method, utilizing magnetometer measurements from a realistic nine-spacecraft observatory. The improved first-order method, which averages over select ensembles of four spacecraft, reconstructs the magnetic field associated with simple current sheets and numerical simulations of turbulence accurately over larger volumes compared to second-order methods or first-order methods using a single regular tetrahedron. Using this averaging method on data sets with fewer than nine measurement points, the volume of accurate reconstruction compared to a known magnetic vector field improves approximately linearly with the number of measurement points.
79 ASTRONOMY AND ASTROPHYSICS↗
Improved accuracy in degenerate variational integrators for guiding centre and magnetic field line flow
First-order-accurate degenerate variational integration (DVI) was introduced in Ellison et al. ( Phys. Plasmas , vol. 25, 2018, 052502) for systems with a degenerate Lagrangian, i.e. one in which the velocity-space Hessian is singular. In this paper we introduce second-order-accurate DVI schemes, both with and without non-uniform time stepping. We show that it is not in general possible to construct a second-order scheme with a preserved two-form by composing a first-order scheme with its adjoint, and discuss the conditions under which such a composition is possible. We build two classes of second-order-accurate DVI schemes. We test these second-order schemes numerically on two systems having non-canonical variables, namely the magnetic field line and guiding centre systems. Variational integration for Hamiltonian systems with non-uniform time steps, in terms of an extended phase space Hamiltonian, is generalized to non-canonical variables. It is shown that preservation of proper degeneracy leads to single-step (one-step) methods without parasitic modes, i.e. to non-uniform time step DVIs. This extension applies to second-order-accurate as well as first-order schemes, and can be applied to adapt the time stepping to an error estimate.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Overset meshes for incompressible flows: On preserving accuracy of underlying discretizations
This study on overset meshes for incompressible-flow simulations is motivated by accurate prediction of wind farm aerodynamics involving large motions and deformations of components with complex geometry. Specifically, using first-order hyperbolic and elliptic equation proxies for the incompressible Navier-Stokes (NS) equations, we investigate the influence of information exchange between overset meshes on numerical performance where the underlying discretization is second-order accurate. The first aspect of information exchange surrounds interpolation of solution where we examine Lagrange and point-cloud-based interpolation for creating constraint equations between overset meshes. To maintain overall second-order accuracy, higher-order interpolation is required for elliptic problems, but linear interpolation is sufficient for hyperbolic problems in first-order form. Higher-order point-cloud-based interpolation provides a pathway to maintaining accuracy in unstructured meshes, but at higher complexity. The second aspect of information exchange focuses on comparing the approaches of overset single system (OSS) and overset Additive Schwarz (OAS) for coupling the linear systems of the overlapping meshes. While the former involves a single linear system, in the latter the discrete linear systems are solved separately, and solving the global system is accomplished through outer iterations and sequential information exchange in a Jacobi fashion. For the test cases studied, accuracy for hyperbolic problems is maintained by performing two outer iterations, whereas many outer iterations are required for elliptic systems. The order-of-accuracy studies explored here are critical for verifying the overset-mesh coupling algorithms used in engineering simulations. Accuracy of these simulations themselves is, however, quantified using engineering quantities of interest such as drag, power, etc. Consequently, we conclude with numerical experiments using NS equations for incompressible flows where we show that linear interpolation and few outer iterations are sufficient for achieving asymptotic convergence of engineering quantities of interest.
97 MATHEMATICS AND COMPUTING↗
Lack of robustness and accuracy of many numerical schemes for phase-field simulations
In this paper, we study the stability, accuracy and convergence behavior of various numerical schemes for phase-field modeling through a simple ODE model. Both theoretical analysis and numerical experiments are carried out on this ODE model to demonstrate the limitation of most numerical schemes that have been used in practice. One main conclusion is that the first-order fully implicit scheme is the only robust algorithm for phase-field simulations while all other schemes (that have been analyzed) may have convergence issue if the time step size is not exceedingly small. More specifically, by rigorous analysis in most cases, we have the following conclusions: (i) The first-order fully implicit scheme converges to the correct steady state solution for all time step sizes. In the case of multiple solutions, one of the solution branches always converges to the correct steady state solution. (ii) The first-order convex splitting scheme, which is equivalent to the first-order fully implicit scheme with a different time scaling, always converges to the correct steady state solution but may seriously lack numerical accuracy for transient solutions. (iii) For the second-order fully implicit and convex splitting schemes, for any time step size $δt > 0$, there exists an initial condition $u_0$ , with $|u_0| > 1$, such that the numerical solution converges to the wrong steady state solution. (iv) For $|u_0|$ ≤ 1, all second-order schemes studied in this paper converge to the correct steady state solution although severe numerical oscillations occur for most of them if the time step size is not sufficiently small. (v) An unconditionally energy-stable scheme (such as the modified Crank–Nicolson scheme) is not necessarily better than a conditionally energy-stable scheme (such as the Crank–Nicolson scheme). Finally, most, if not all, of the above conclusions are expected to be true for more general Allen–Cahn and other phase-field models.
97 MATHEMATICS AND COMPUTING↗