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427 records · Page 24

Implementing the three-particle quantization condition for π + π + K + and related systems

Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O(1/L 5 ); and we calculate the leading-order predictions in chiral perturbation theory for K df,3 in the π + π + K + and π + K + K + systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π + π + K + levels using the two- and three-particle interactions predicted by chiral perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Correlating Mechanical Sensitivity with Spin Transition in the Explosive Spin Crossover Complex [Fe(Htrz) 3 ] n [ClO 4 ] 2 n

Spin crossover complexes are known to undergo bond length, volume, and enthalpy changes during spin transition. In an explosive spin crossover complex, these changes could affect the mechanical and initiation sensitivity of the explosive and lead to the development of a new class of sensitivity switchable materials. To explore this relationship, the well-known spin crossover compound [Fe(Htrz) 3 ] n [ClO 4 ] 2n (1) was re-evaluated for its explosive properties, and its mechanical impact sensitivity was correlated to spin transition. A variable temperature impact test was developed and used to evaluate the impact sensitivity of 1 in the low spin (LS, S = 0), thermally accessed high spin (HS, S = 2), and mixed LS and HS states. For comparison, the structurally similar Ni compound, [Ni(Htrz) 3 ] n [ClO 4 ] 2n (2), which does not undergo a spin transition at accessible temperatures, was synthesized and characterized, and its explosive properties and variable temperature impact sensitivity measured. These results reveal a correlation between impact sensitivity and spin transition, where 1 exhibits lower impact sensitivity in the LS state and increases in sensitivity upon transition to the HS state. Here, density functional theory was used to predict structural changes that occur upon spin transition that correlate to the change in sensitivity. This demonstrates, for the first time, an explosive spin crossover compound (ExSCO) that exhibits switchable impact sensitivity with a fully reversible internal switching mechanism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Semi-implicit method to solve compressible multiphase fluid flows without acoustic time step restrictions

A new 3D multiphase numerical capability is presented here for simulating multiphase flow regimes at all Mach numbers (M). The new method is a semi-implicit extension of the finite volume discrete equation method (DEM) of Chinnaya et al. (2004), which originally used explicit time-stepping. The capability is also developed to work with another extension of the DEM to moving grids for arbitrary Lagrangian-Eularian (ALE) methods detailed in Dunn (2011). Rather than solving all phase equations simultaneously, the DEM reduces the equations to a system of single-phase Riemann solves, where each phase has its own velocity and thermodynamic state. Exchanges between the phases are modeled through source terms accounting for the phase interactions. Furthermore, since the original multiphase scheme uses an explicit time-advancement scheme, it has time step restrictions dictated by the speed of sound, which limits the model's ability to simulate weakly compressible flows which typically need to be integrated for longer time periods. Here, we extend the current multiphase formulation by implementing a pressure-correcting step to enable implicit calculations and remove acoustic time step limitations. The new semi-implicit algorithm allows use of relatively large time steps compared to an explicit method. Validation and benefits of the new implicit time-step method are illustrated using several examples including weakly compressible flows and strong shock waves. The scheme presented here is general and may be used for a variety of applications which require capabilities for handling multiphase flow at a wide range of Mach numbers. However, the goal of this research is to simulate all stages of high energy explosions, including the shock formation (high Mach numbers) and evolution of the buoyant cloud (low Mach numbers).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Designing high-performance superconductors with nanoparticle inclusions: Comparisons to strong pinning theory

One of the most promising routes for achieving high critical currents in superconductors is to incorporate dispersed, non-superconducting nanoparticles to control the dissipative motion of vortices. However, these inclusions reduce the overall superconducting volume and can strain the interlaying superconducting matrix, which can detrimentally reduce T c . Consequently, an optimal balance must be achieved between the nanoparticle density n p and size d. Determining this balance requires garnering a better understanding of vortex–nanoparticle interactions, described by strong pinning theory. Here, we map the dependence of the critical current on nanoparticle size and density in (Y 0.77 , Gd 0.23 )Ba 2 Cu 3 O 7-δ films in magnetic fields of up to 35 T and compare the trends to recent results from time-dependent Ginzburg–Landau simulations. We identify consistency between the field-dependent critical current J c (B) and expectations from strong pinning theory. Specifically, we find that J c ∝ B -α , where α decreases from 0.66 to 0.2 with increasing density of nanoparticles and increases roughly linearly with nanoparticle size d/ξ (normalized to the coherence length). At high fields, the critical current decays faster (~B -1 ), suggesting that each nanoparticle has captured a vortex. When nanoparticles capture more than one vortex, a small, high-field peak is expected in J c (B). Due to a spread in defect sizes, this novel peak effect remains unresolved here. Finally, we reveal that the dependence of the vortex creep rate S on nanoparticle size and density roughly mirrors that of α, and we compare our results to low-T nonlinearities in S(T) that are predicted by strong pinning theory.

36 MATERIALS SCIENCE↗

Erosion of focus rings in capacitively coupled plasma etching reactors

In plasma etching reactors, the structure surrounding the wafer, often called a focus ring (FR), plays an important role in maintaining uniform fluxes of reactants across the wafer. The FR is typically made of dielectric materials. During the plasma etching process, the sheath that forms over the wafer to accelerate ions anisotropically into the surface extends over the FR. Electrical charging of the FR modifies the sheath relative to that over the wafer. On the one hand, one wants the sheath to be uniform across the wafer-FR boundary to enable uniform fluxes to the edge of the wafer. On the other hand, maintaining a high voltage sheath over the FR will erode the FR, which is undesirable as the FR is a consumable component that must be periodically replaced in high volume manufacturing. In this work, we computationally investigated the consequences of dielectric constant ε of the FR materials on erosion of the FR. The series capacitance of the FR and its underlying structure is typically smaller than that of the wafer and its underlying structure. As a result, the FR charges quickly relative to the wafer, which then reduces the voltage across the sheath on top of the FR. The ion energy and angular distributions (IEADs) striking the FR are, therefore, generally lower in energy with a broader angular distribution. With ε = 2, the ion energies striking the middle to the outer edge of the FR are 30–180 eV, whereas for ε = 100, the ion energies are 120–380 eV. At the transition between the wafer and the FR, there is a skew in the IEAD as large as 15° that results from the difference in sheath thickness above the wafer and the FR. This skew and the erosion rate across the FR are functions of the dielectric constant of the FR material. With low ε, the FR charges quickly, less plasma is produced above the FR, and there is less voltage across the sheath that results in less FR erosion. Increasing ε of the FR produces a higher sheath voltage as well as higher ion fluxes over the FR, which increases erosion, while the skew at the edge of the wafer is less severe. Further, the material of the subsurface portion of the FR, which dominates its capacitance, is an important consideration in the design of the substrate assembly.

36 MATERIALS SCIENCE↗

ORNL_AISD_NiNb

This dataset describes the nickel-niobium solid solution binary alloy, where the two constituent elements nickel (Ni) and niobium (Nb) are randomly placed on an underlying crystal lattice. This dataset for nickel-niobium (Ni-Nb) alloys available includes the formation energy and bulk modulus for each crystal structure. Each atomic sample has a disordered phase which is obtained starting from an initial regular crystal structure of type body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal compact packed (HCP). The geometry optimization ensures that all the alloy samples reached the equilibrium with negative formation energy. We perform geometry optimizations using the LAMMPS simulation package [1], a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. We utilized the embedded atom model (EAM) potential for Ni and Nb developed in a previous study [2]. The potential could describe behaviors of the liquid and solid phases of Ni-Nb alloy. The structural factors and angular distributions of three atoms are well-matched with X-ray and ab initio-based molecular dynamics data. We prepared the three different crystals with different initial lattice parameters (3.52 Ã… for FCC, 3.32 Ã… for BCC, and 3.5 Ã… for HCP). We performed energy minimization in two steps. Firstly, we minimized the structures with an isotropic unit cell to minimize the side effects from our arbitrary lattice parameters for all other compositions. Then, we applied geometry optimization with a triclinic (non-orthogonal) unit cell to fully minimize the stress components to calculate the elastic constants. In this procedure, we chose 10,000 as the maximum number of allowable steps aimed at obtaining fully relaxed atomic geometries. The dataset consists of three sets of crystal structures. The first set contains 46,086 irregular crystal structures, each of them with 54 atoms, obtained through optimization starting from a regular BCC crystal structure. The second set contains 24,543 irregular crystal structures, each of them with 32 atoms, obtained through optimization starting from a regular FCC crystal structure. The third set contains 39,303 irregular crystal structures, each of them with 48 atoms, obtained through optimization starting from a regular HCP crystal structure. The atomic configurations within each set span the possible compositional range. The three sets have been unified in a global dataset, which is extremely heterogeneous in terms of crystal structures, lattice volumes, and atomic configurations. Organization of files inside the dataset: the dataset contains three subdirectories called • BCC_opt • FCC_opt • HCP_opt based on the type of initial regular structure used to start the geometry optimization. Inside each of these folders, every atomic structure is identified by a string “A_B_Câ€, where A denotes the number of Nb in the system, B denotes index of structure with a given Nb number, and C denotes the total number of structures generated with a given Nb number. For each optimized crystal structure identified by the unique string of characters “A_B_Câ€, three files are provided: • A_B_C_opt.xyz: The optimized geometries in xyz format • A_B_C_opt.cfg: The optimized geometries in cfg format. It includes cell information and atomic energy, and forces calculated from LAMMPS. • A_B_C.elastic: Raw data of 21 elastic constants from LAMMPS output. • A_B_C.bulk: Calculated upper and lower bounds of bulk modulus and averaged one based on Voigt-Reuss-Hill approach from *.elastic. References: [1] A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comp. Phys. Comm., 271:108171, 2022. [2] Y Zhang, R Ashcraft, MI Mendelev, CZ Wang, and KF Kelton. Experimental and molecular dynamics simulation study of structure of liquid and amorphous ni62nb38 alloy. The Journal of chemical physics, 145(20):204505, 2016.

36 MATERIALS SCIENCE↗

Experimental and Theoretical Confirmation of Covalent Bonding in α‐Pu

Plutonium's radioactivity provides functionality for nuclear batteries, nuclear reactors, etc., but its complex electronic properties harbor strongly correlated behavior giving rise to a host of interesting phenomena including the presence of a ca. 25% volume collapse between δ-Pu and α-Pu. The complex bonding environments of the ground state allotrope, α-Pu, serve as a unique testing ground for new computational and experimental approaches within the Pu science community. For the first time, a combination of novel ansatzes is used in all-electron density functional theory (DFT) and pair distribution functions (PDF) obtained from high-Q X-ray diffraction to study the bonding behavior in α-Pu. This first experimental and theoretical co-informed description of local bonding behavior for α-Pu reveals covalent bonds, which is a topic that remains of interest in this allotrope. The covalent bonding present at the atomistic level accounts for several of α-Pu's macropscopic properties (e.g., Poisson's ratio) that in turn explains its physical functionalities relative to other allotropic phases like δ-Pu.

36 MATERIALS SCIENCE↗

Observation of the distribution of nuclear magnetization in a molecule

Precise experimental control and interrogation of molecules and calculations of their structure are enriching the investigation of nuclear and particle physics phenomena. Molecules containing heavy, octupole-deformed nuclei, such as radium, are of particular interest. Here, we report precision laser spectroscopy measurements and theoretical calculations of the structure of the radioactive radium monofluoride molecule 225 Ra 19 F. Our results reveal fine details of the short-range electron-nucleus interaction, indicating the high sensitivity of this molecule to the distribution of magnetization, within the radium nucleus. Here, these results provide a stringent test of the description of the electronic wave function inside the nuclear volume, highlighting the suitability of these molecules for investigating subatomic phenomena.

Nuclear structure↗

Spirometric traits show quantile-dependent heritability, which may contribute to their gene-environment interactions with smoking and pollution

Background: “Quantile-dependent expressivity” refers to a genetic effect that is dependent upon whether the phenotype (e.g., spirometric data) is high or low relative to its population distribution. Forced vital capacity (FVC), forced expiratory volume in 1 second (FEV 1 ), and the FEV 1 /FVC ratio are moderately heritable spirometric traits. The aim of the analyses is to test whether their heritability (h 2 ) is constant over all quantiles of their distribution. Methods: Quantile regression was applied to the mean age, sex, height and smoking-adjusted spirometric data over multiple visits in 9,993 offspring-parent pairs and 1,930 sibships from the Framingham Heart Study to obtain robust estimates of offspring-parent (β OP ), offspring-midparent (β OM ), and full-sib regression slopes (β FS ). Nonparametric significance levels were obtained from 1,000 bootstrap samples. β OP s were used as simple indicators of quantile-specific heritability (i.e.,h 2 = 2β OP /(1+r spouse ), where r spouse was the correlation between spouses). Results: β OP ± standard error (SE) decreased by 0.0009 ± 0.0003 (P = 0.003) with every one-percent increment in the population distribution of FEV 1 /FVC, i.e., β OP ± SE were: 0.182 ± 0.031, 0.152 ± 0.015; 0.136 ± 0.011; 0.121 ± 0.013; and 0.099 ± 0.013 at the 10th, 25th, 50th, 75th, and 90th percentiles of the FEV 1 /FVC distribution, respectively. These correspond to h 2 ± SEs of 0.350 ± 0.060 at the 10th, 0.292 ± 0.029 at the 25th, 0.262 ± 0.020 at the 50th, 0.234 ± 0.025 at the 75th, and 0.191 ± 0.025 at the 90th percentiles of the FEV 1 /FVC ratio. Maximum mid-expiratory flow (MMEF) h 2 ± SEs increased 0.0025 ± 0.0007 (P = 0.0004) with every one-percent increment in its distribution, i.e.: 0.467 ± 0.046, 0.467 ± 0.033, 0.554 ± 0.038, 0.615 ± 0.042, and 0.675 ± 0.060 at the 10th, 25th, 50th, 75th, and 90th percentiles of its distribution. This was due to forced expiratory flow at 75% of FVC (FEF75%), whose quantile-specific h 2 increased an average of 0.0042 ± 0.0008 for every one-percent increment in its distribution. It is speculated that previously reported gene-environment interactions may be partially attributable to quantile-specific h 2 , i.e., greater heritability in individuals with lower FEV 1 /FVC due to smoking or airborne particles exposure vs. nonsmoking, unexposed individuals. Conclusion: Heritabilities of FEV 1 /FVC, MMEF, and FEF75% from quantile-regression of offspring-parent and sibling spirometric data suggest their quantile-dependent expressivity.

59 BASIC BIOLOGICAL SCIENCES↗

Hydro-Code Implementation and Testing of a Kinetic Phase Transition Framework

In this report we describe the Kinetic Phase Transition (KPT) framework that has been worked out over the last 10 years (from around 2014) and the implementation of it into three different codes, the one-dimensional hydro- LASLO and the three-dimensional magneto-hydro- ALEGRA, Sandia codes, via subroutines in the LAMBDA Equations of State and constitutive models package, and Flag, an arbitrary Lagrangian-Eulerian multiphysics code developed within the Lagrangian Applications project (LAP) at LANL. We discuss the introduction of phase mass (and/or volume) fractions that are needed in a code for it to be ‘phase aware’, that is, not only the thermodynamic state is known in each point but also the mixture of the materials’ phases in that point. Further we point to the need of a full Equations of State for each phase in a material to achieve phase awareness and we review the equilibrium phase model, where a phase mixture is at its lowest Gibbs free energy state, to make this point clear. Contrasting the kinetic phase transition to this equilibrium model seamlessly introduce us to the KPT framework that is subsequently thoroughly discussed. While the determination of the total state and the states and mass fractions of phases in each point is a problem that can borrow many of its numerical details from Eulerian codes and mixture of materials (not phases), the update of mass fractions with time in a KPT framework needs a new set of considerations. General for any update model is that we need to prevent mass fractions from becoming unphysical (negative or their sum to be larger than one). We have solved this problem by implementing a subdivision of the hydro time step that prevents the phase from being fully present to not present at all in one subdivided time step by limiting the size of the subdivided time step. This scheme also corrects numerical problems from abrupt changes in parameter values, the so called Gibbs phenomena, that gives rise to slushing between phases in the KPT framework. Interspersed throughout the report are discussions on different thermodynamics considerations. EOS validity windows, limitations on the EOS phase space, are needed for the KPT framework and are discussed separately and exemplified. The KPT framework described in this report has been verified by code comparison, but validation is still an active area of research. There is room for improvement in the update model, both in the model for determination of rates and in how to prevent the mass fractions from becoming unphysical. In addition, the parameters in the KPT update model and the placement of the phase boundary in the EOS phase space, and interactions with other constitutive models, are closely related and interfering with each other. One possible way forward is to simultaneously develop KPT parameters, EOS, and constitutive models for each material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Luminosity determination using Z boson production at the CMS experiment

The measurement of Z boson production is presented as a method to determine the integrated luminosity of CMS data sets. The analysis uses proton–proton collision data, recorded by the CMS experiment at the CERN LHC in 2017 at a center-of-mass energy of 13 TeV. Events with Z bosons decaying into a pair of muons are selected. The total number of Z bosons produced in a fiducial volume is determined, together with the identification efficiencies and correlations from the same data set, in small intervals of 20 pb –1 of integrated luminosity, thus facilitating the efficiency and rate measurement as a function of time and instantaneous luminosity. Using the ratio of the efficiency-corrected numbers of Z bosons, the precisely measured integrated luminosity of one data set is used to determine the luminosity of another. For the first time, a full quantitative uncertainty analysis of the use of Z bosons for the integrated luminosity measurement is performed. The uncertainty in the extrapolation between two data sets, recorded in 2017 at low and high instantaneous luminosity, is less than 0.5%. We show that the Z boson rate measurement constitutes a precise method, complementary to traditional methods, with the potential to improve the measurement of the integrated luminosity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗