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DOE OSTI2025

Ergodic Lagrangian dynamics in a superhero universe

We present a fictional scenario that, while undeniably whimsical, provides the foundation for a unique exercise in extended problem solving, physics analysis, and quantitative model development. Starting with the foundational premise of the Wild Cards shared-world superhero universe, we demonstrate how a variety of concepts appropriate to the advanced undergraduate level—ergodicity, functional analysis, Lagrangian mechanics, and the ever-important simplifying approximation—can be combined into a rich, coherent mathematical model. The goal of this case study is to develop a useful pedagogical exercise in exploring an open-ended research question that presents, at first glance, no clear path forward. Being both eclectic and lengthy, this exercise offers a unique way for students to apply their core physics and mathematics education. It is perhaps best used within a senior honors seminar or within a brief (e.g., January term) elective class.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

A general metriplectic framework with application to dissipative extended magnetohydrodynamics

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Nonlinear dynamics from linear quantum evolutions

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given family of states, either as a consequence of experimental constraints or inside an approximation scheme. In this work we investigate such issues in connection with a one parameter group ϕ{sub t} of transformations on a Hilbert space, H, defining the unitary evolutions of a chosen quantum system. Two procedures will be presented: the first one consists in the restriction of the vector field associated with the Schrödinger equation to a submanifold invariant under the flow ϕ{sub t}. The second one makes use of the Lagrangian formalism and can be extended also to non-invariant submanifolds, even if in such a case the resulting dynamics is only an approximation of the flow ϕ{sub t}. Such a result, therefore, should be conceived as a generalization of the variational method already employed for stationary problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Ab Initio Direct Dynamics

The reactivity and dynamics of molecular systems can be explored computationally by classical trajectory calculations. The traditional approach involves fitting a functional form of a potential energy surface (PES) to the energies from a large number of electronic structure calculations and then integrating numerous trajectories on this fitted PES to model the molecular dynamics. The ever-decreasing cost of computing and continuing advances in computational chemistry software have made it possible to use electronic structure calculations directly in molecular dynamics simulations without first having to construct a fitted PES. In this “on-the-fly” approach, every time the energy and its derivatives are needed for the integration of the equations of motion, they are obtained directly from quantum chemical calculations. This approach started to become practical in the mid-1990s as a result of increased availability of inexpensive computer resources and improved computational chemistry software. The application of direct dynamics calculations has grown rapidly over the last 25 years and would require a lengthy review article. The present Account is limited to some of our contributions to methods development and various applications. To improve the efficiency of direct dynamics calculations, we developed a Hessian-based predictor-corrector algorithm for integrating classical trajectories. Hessian updating made this even more efficient. Furthermore, this approach was also used to improve algorithms for following the steepest descent reaction paths. For larger molecular systems, we developed an extended Lagrangian approach in which the electronic structure is propagated along with the molecular structure. Strong field chemistry is a rapidly growing area, and to improve the accuracy of molecular dynamics in intense laser fields, we included the time-varying electric field in a novel predictor-corrector trajectory integration algorithm. Since intense laser fields can excite and ionize molecules, we extended our studies to include electron dynamics. Specifically, we developed code for time-dependent configuration interaction electron dynamics to simulate strong field ionization by intense laser pulses. Our initial application of ab initio direct dynamics in 1994 was to CH 2 O → H 2 + CO; the calculated vibrational distributions in the products were in very good agreement with experiment. In the intervening years, we have used direct dynamics to explore energy partitioning in various dissociation reactions, unimolecular dissociations yielding three fragments, reactions with branching after the transition state, nonstatistical dynamics of chemically activated molecules, dynamics of molecular fragmentation by intense infrared laser pulses, selective activation of specific dissociation channels by aligned intense infrared laser fields, angular dependence of strong field ionization, and simulation of sequential double ionization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

PYSEQM

PYSEQM is a package for performing semi-empirical quantum mechanical (SEQM) simulations on molecular systems utilizing PyTorch. SEQM simulations determine molecular properties (energy, electron density, dipole moment, ect.) by solving an approximate Schrödinger equation for the motions of electrons in a molecule. The use of PyTorch provides three specific advantages. First, it allows the calculations to be offloaded to GPU accelerators, giving an order of magnitude increase in speed. Second, back propagation is used to get atomic forces (derivative of the total energy with respect to atomic position) at the same computational cost as the energy calculation itself. Finally, the use of PyTorch makes for a natural interface to modern machine learning methods, which can be used to adjust the semi-empirical parameters build into SEQM methods. Additionally, PYSEQM implements various other optimizations for performing quantum mechanics based molecular dynamics, including SP2 for rapid GPU based solution of the self-consistent field algorithm, and the extended Lagrangian method for rapid QM-MD.

Nebgen, Benjamin↗

DOE OSTI2024

Small arms suppression project (LLNL final report)

US Special Operations Command (USSOCOM) was seeking a technological leap in small firearms weapon suppressor technology, because anticipated enemy capabilities are requiring the operators to have smaller detection cross sections to ensure the safe execution of missions. Suppressors have been developed almost exclusively through trial-and-error methods since the time of the original design by Hiram Maxim over one hundred years ago. Consequently USSOCOM deemed it prudent to perform a physicsbased study of weapon suppression to understand performance limits and possibly identify breakthrough technologies. Lawrence Livermore National Laboratory’s (LLNL’s) high performance production level computational tool called ALE3D (Arbitrary Lagrangian-Eulerian 3D and 2D) has unique physics models and numerical algorithms for modeling suppressor dynamics. The flexible and extendable code framework supports fully integrated hydrodynamics, heat transfer, solid and fluid dynamics, and chemistry that can be applied to simulating propellant-driven motion of a bullet down a gun barrel, the transfer of heat from the burning propellant to the barrel and suppressor, the chemistry of muzzle flash, and the shock/acoustic/optical signatures in the near-field. LLNL’s originally anticipated role was to augment ALE3D for this task, by developing the software and analysis methodologies specific to the simulation of blast and muzzle flash phenomena. It was believed that insights provided by our ALE3D simulations in tandem with a coordinated experimental component by our other team members from Oak Ridge National Laboratory (ORNL) and the U. S. Army Armament, Research, Development and Engineering Center (ARDEC), would have excellent prospects of yielding useful suppressor design improvements that could be transitioned to industry and utilized by US Special Operations Command. The three year effort has come to fruition with the development of revolutionary suppressor designs that far outperform any previous or current design by anyone outside this multi-lab team.

42 ENGINEERING↗

DOE OSTI2024

Sequential formulation of all‐way coupled finite strain thermoporomechanics for largely deformable gas hydrate deposits

We develop a numerically stable sequential formulation of thermoporomechanics for largely deformable gas hydrate deposits, extended from the fixed stress split of infinitesimal transformation. Constitutive equations are based on the total Lagrangian approach for both flow and geomechanics, including dynamic full tensor permeability and thermal conductivity updated from the deformation gradient. For space discretization, we take the cell-centered finite volume and node-based finite element method for flow and geomechanics, respectively. Then, we propose a sequential implicit method for all-way coupled thermoporomechanics, where the nonisothermal multiphase flow problem of gas hydrates is solved implicitly first and then the geomechanics problem is solved implicitly at the next step. During solution of the flow problem, we fix the rate of first Pioal total stress for numerical stability as well as apply porosity correction and entropy correction to account for geomechanical effects. We test numerical examples where flow and geomechanics parameters are based on deep oceanic gas hydrate deposits. When applying depressurization, even though the results between the infinitesimal transformation and finite strain geomechanics are similar in the early stages due to small deformation, we find differences between them in the late times as deformation becomes large. Accordingly, permeability and thermal conductivity tensors become nonisotropic full tensors although they are initially isotropic. Furthermore, we identify numerical stability of the developed sequential method from the test cases that exhibit the highly complex coupled gas hydrate systems with large deformation. Thus, the proposed sequential formulation can be applied in largely deformable gas hydrate systems.

42 ENGINEERING↗

DOE OSTI2021

A fourth-order Lagrangian discontinuous Galerkin method using a hierarchical orthogonal basis on curvilinear grids

The existing high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic methods are restricted to using quadratic meshes with quadratic polynomials (P2), which in turn, yield up to third-order accuracy. Additionally, these existing DG hydrodynamic schemes, when extended to work with cubic meshes and cubic polynomials (P3), can be unstable on strong-shock problems. Therefore, this paper presents a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method to simulate compressible material dynamics ( e.g., gasses, fluids, and solids) with strong-shocks using cubic meshes and cubic polynomials, and delivers up to fourth-order accuracy on smooth flows. The stability on shock problems is achieved using new hierarchical orthogonal basis functions and a new subcell mesh stabilization (SMS) scheme for cubic meshes. The accuracy and robustness of the new high-order accurate Lagrangian DG hydrodynamic method is demonstrated by simulating a diverse suite of challenging test problems covering gas and solid dynamic problems on curvilinear meshes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Physics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor

Reduced models describing the Lagrangian dynamics of the velocity gradient tensor (VGT) in homogeneous isotropic turbulence (HIT) are developed under the physics-informed machine learning (PIML) framework. We consider the VGT at both Kolmogorov scale and coarse-grained scale within the inertial range of HIT. Building reduced models requires resolving the pressure Hessian and subfilter contributions, which is accomplished by constructing them using the integrity bases and invariants of the VGT. The developed models can be expressed using the extended tensor basis neural network (TBNN) introduced by Ling et al. [J. Fluid Mech. 807, 155 (2016)]. Physical constraints, such as Galilean invariance, rotational invariance, and incompressibility condition, are thus embedded in the models explicitly. Our PIML models are trained on the Lagrangian data from a high-Reynolds number direct numerical simulation (DNS). To validate the results, we perform a comprehensive out-of-sample test. We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the “ground-truth” DNS data. A number of other important features describing the structure of HIT are reproduced by the model successfully. We have also identified challenges in modeling inertial range dynamics, which indicates that a richer modeling strategy is required. This helps us identify important directions for future research, in particular towards including inertial range geometry into the TBNN.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Reduced scale stripline platform to extend accessible pressures on the Z machine: Shockless compression of platinum to 650 GPa

Reaching astrophysically relevant high energy density (HED) material states in the laboratory is an ongoing effort at multiple experimental facilities. We have developed a new dynamic compression platform for the Z Pulsed Power Facility that allows for sample sizes 100s of [Formula: see text]m in thickness that accommodate multiple grains in order to fully capture bulk properties, such as material strength. A pair of experiments compressed platinum (Pt) to HED conditions and conventional inverse Lagrangian analysis as well as a recent Bayesian calibration technique were used to determine the principal isentrope to 650 GPa with density uncertainties of <2%. These low uncertainties are calculated for single sample experiments, presenting the possibility of even smaller experimental uncertainties with multiple samples the platform allows. Our new platform extends the accessible Pt ramp pressures achievable on the Z machine to over 80% of the pressure recently achieved using the National Ignition Facility planar Hohlraum platform. This new capability, the next generation evolution of the stripline platform, was made possible by advancements in both our understanding of the Z pulsed power driver and our overall magnetohydrodynamic modeling capabilities.

Porwitzky, Andrew↗

DOE OSTI2021

Population balance modeling of polyurethane foam formation with pressure‐dependent growth kernel

Abstract Polyurethane foams are widely used materials often chosen for their useful characteristics such as low thermal conductivity, ease of application, and high strength‐to‐weight ratios. Computational models are needed to predict the dynamics of the flow and expansion, and the resulting material properties, to improve manufacturing processes. In this paper, a model for PMDI, a water‐blown polyurethane foam, is presented. By extending a kinetics‐based approach by adding bubble‐scale information via a population balance equation (PBE) using the quadrature method of moments, we can track bubble size distributions during foaming. We present results from a three‐dimensional computational fluid dynamics model using arbitrary Lagrangian–Eulerian interface tracking implemented in finite element software. The model compares favorably with experimental data, including dynamics, bubble distributions measured by both camera and diffusion wave spectroscopy, and post‐test bubble size from scanning electron microscopy and density measurements from x‐ray computed tomography.

Ortiz, Weston↗

DOE OSTI2025

Bulk viscosity of two-flavor color superconducting quark matter in neutron star mergers

This work investigates the bulk viscosity of warm, dense, neutrino-transparent, color-superconducting quark matter, where damping of density oscillations in the kHz frequency range arises from weak-interaction-driven direct Urca processes involving quarks. We study the two-flavor red-green paired color-superconducting (2SC) phase, while allowing for the presence of unpaired strange quarks and blue color light quarks of all flavors. Our calculations are based on the SU(3) Nambu–Jona–Lasinio model, extended to include both vector interactions and the ‘t Hooft determinant term. The primary focus is on how variations in the NJL Lagrangian parameters—specifically, the diquark and vector coupling strengths—affect both the static properties of quark matter, such as its equation of state and composition, and its dynamical behavior, including bulk viscosity and associated damping timescales. We find that the bulk viscosity and corresponding damping timescale can change by more than an order of magnitude upon varying the vector coupling by a factor of two at high densities and by a lesser degree at lower densities. This sensitivity primarily arises from the susceptibility of 2SC matter, with a smaller contribution from modifications to the weak interaction rates. In comparison, changes in the diquark coupling have a more limited impact. The damping of density oscillations in 2SC matter is similar quantitatively to nucleonic matter and can be a leading mechanism of dissipation in merging hybrid stars containing color superconducting cores.

Gravitational Waves↗

DOE OSTI2021

Intermittent Frontogenesis in the Alboran Sea

Abstract We present a phenomenological description and dynamical analysis of the Alboran fronts using a realistic simulation at submesoscale resolution. The study is focused on east Alboran fronts emerging within relatively strong flows that separate from the Spanish coast into the basin interior. Despite modest lateral shifting associated with the position of the Alboran anticyclonic gyres and variations in intensity, these fronts present a similar structure and dynamical configuration as the climatological Almeria–Oran front. The statistical analysis of our solution shows that strained-induced frontogenesis is a recurrent submesoscale mechanism associated with these fronts, and the process is assessed in terms of the advective Lagrangian frontogenetic tendencies associated with buoyancy and velocity horizontal gradients. Intermittency in their strength and patterns is indicative of high variability in the occurrence of active frontogenesis in association with the secondary (overturning) circulation across the frontal gradient. As a result, we find many episodes with strong surface fronts that do not have much associated downwelling. Frontogenesis and the associated secondary circulation are further explored during two particular frontal events, both showing strong downwelling of (1) cm s −1 extending down into the pycnocline. A frontogenetic contribution of turbulent vertical momentum mixing to the secondary circulation is identified in the easternmost region during the cold season, when the dynamics are strongly influenced by the intrusion of the salty Northern Current. The background vertical velocity fields observed during the analyzed events indicate other currents in the submesoscale range, including tidal and topographic internal waves.

Capó, Esther↗

DOE OSTI2021

Stability of trapped solutions of a nonlinear Schrödinger equation with a nonlocal nonlinear self-interaction potential

This work focuses on the study of the stability of trapped soliton-like solutions of a (1 + 1)-dimensional nonlinear Schrödinger equation (NLSE) in a nonlocal, nonlinear, self-interaction potential of the form [|Ψ(x,t)| 2 +|Ψ(-x,t)| 2 ] κ where κ is an arbitrary nonlinearity parameter. Although the system with κ = 1 (i.e. fully integrable case) was first reported by Yang (2018 Phys. Rev. E 98 042202), here in the present work, we extend this model to the one in which κ is arbitrary. This allows us to compare the stability properties of the now trapped solutions to previously found solutions of the more usual NLSE with κ ≠ 1 which are moving soliton solutions. We show that there is a simple, one-component, nonlocal Lagrangian and corresponding action governing the dynamics of the system. Using a collective coordinate method derived from the action as well as assuming the validity of Derrick's theorem, we find that these trapped solutions are stable for 0 < κ < 2 and unstable when κ > 2. At the critical value of κ, i.e. κ = 2, the solution can either collapse or blowup linearly in time when q 0 = 0, where q 0 is the center of the initial density ρ(x, t = 0) = ψ*ψ of the solution. For q 0 ≠ 0 the displaced solution collapses. When κ > 2 initial small displacements from the origin also lead to collapse of the wave function. This phenomenon is not seen in the usual NLSE.

collective coordinates↗

DOE OSTI2021

A Lagrangian Study of Interfaces at the Edges of Cumulus Clouds

Abstract Interfaces at the edge of an idealized, nonprecipitating, warm cloud are studied using direct numerical simulation (DNS) complemented with a Lagrangian particle tracking routine. Once a shell has formed, four zones can be distinguished: the cloud core, visible shell, invisible shell, and the environment. The union of the visible and invisible regions is the shell commonly referred to in literature. The boundary between the invisible shell and the environment is the turbulent–nonturbulent interface (TNTI), which is typically not considered in cloud studies. Three million particles were seeded homogeneously across the domain and properties were recorded along individual trajectories. The results demonstrate that the traditional cloud boundary (separating cloudy and noncloudy regions using thresholds applied on liquid condensate or updraft velocity) are some distance away from the TNTI. Furthermore, there is no dynamic difference between the traditional liquid-condensate boundary and the region extending to the TNTI. However, particles crossing the TNTI exhibit a sharp jump in enstrophy and a smooth increase in buoyancy. The traditional cloud boundary coincides with the location of minimum buoyancy in the shell. The shell premixes the entraining and detraining air and analysis reveals a highly skewed picture of entrainment and detrainment at the traditional cloud boundary. A preferential entrainment of particles with velocity and specific humidity higher than the mean values in the shell is observed. Large-eddy simulation of a more realistic setup detects an interface with similar properties using the same thresholds as in the DNS, indicating that the DNS results extrapolate beyond their idealized conditions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Background-field Method and QCD Factorization

One method for deriving a factorization for QCD processes is to use successive integration over fields in the functional integral. In this approach, we separate the fields into two categories: dynamical fields with momenta above a relevant cutoff, and background fields with momenta below the cutoff. The dynamical fields are then integrated out in the background of the low-momentum background fields. This strategy works well at tree level, allowing us to quickly derive QCD factorization formulas at leading order. However, to extend the approach to higher loops, it is necessary to rigorously define the functional integral over dynamical fields in an arbitrary background field. This framework was carefully developed for the calculation of the effective action in a background field at the two-loop level in the classic paper by Abbott «The Background Field Method Beyond One Loop», Nucl. Phys. B 185 , 189 (1981). Building on this work, I specify the renormalized background-field Lagrangian and define the notion of the quantum average of an operator in a background field, consistent with the “separation of scales” scheme mentioned earlier. As examples, I discuss the evolution of the twist-2 gluon light-ray operator and the one-loop gluon propagator in a background field near the light cone.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N-body mock challenge for the eBOSS emission line galaxy sample

ABSTRACT Cosmological growth can be measured in the redshift space clustering of galaxies targeted by spectroscopic surveys. Accurate prediction of clustering of galaxies will require understanding galaxy physics, which is a very hard and highly non-linear problem. Approximate models of redshift space distortion (RSD) take a perturbative approach to solve the evolution of dark matter and galaxies in the universe. In this paper, we focus on extended Baryon Oscillation Spectroscopic (eBOSS) emission line galaxies (ELGs) that live in intermediate mass haloes. We create a series of mock catalogues using haloes from the Multidark and outer rim dark matter only N-body simulations. Our mock catalogues include various effects inspired by baryonic physics such as assembly bias and the characteristics of satellite galaxies kinematics, dynamics, and statistics deviating from dark matter particles. We analyse these mocks using the TNS RSD model in Fourier space and the convolution Lagrangian perturbation theory (CLPT) in configuration space. We conclude that these two RSD models provide an unbiased measurement of RSD within the statistical error of our mocks. We obtain the conservative theoretical systematic uncertainty of $3.3{{\ \rm per\ cent}}$, $1.8{{\ \rm per\ cent}}$, and $1.5{{\ \rm per\ cent}}$ in fσ8, α∥, and α⊥, respectively, for the TNS and CLPT models. We note that the estimated theoretical systematic error is an order of magnitude smaller than the statistical error of the eBOSS ELG sample and hence are negligible for the purpose of the current eBOSS ELG analysis.

Alam, Shadab↗