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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green’s function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as “black-box” simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green’s function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicit

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Algebraic motion of vertically displacing plasmas

In this paper, the vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear “sinking” behaviour shown to be algebraic and decelerating. Finally, the acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quench dynamics precipitating loss of plasma current.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

On simulation of local fluxes in molecular junctions

We present a pedagogical review of the current density simulation in molecular junction models indicating its advantages and deficiencies in analysis of local junction transport characteristics. In particular, we argue that current density is a universal tool which provides more information than traditionally simulated bond currents, especially when discussing inelastic processes. However, current density simulations are sensitive to the choice of basis and electronic structure method. We note that while discussing the local current conservation in junctions, one has to account for the source term caused by the open character of the system and intra-molecular interactions. Our considerations are illustrated with numerical simulations of a benzenedithiol molecular junction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Sesame-style decomposition of KS-DFT molecular dynamics for direct interrogation of nuclear models

A common paradigm used in the construction of equations of state is to decompose the thermodynamics into a superposition of three terms: a static-lattice cold curve, a contribution from the thermal motion of the nuclei, and a contribution from the thermal excitation of the electrons. While statistical mechanical models for crystals provide tractable framework for the nuclear contribution in the solid phase, much less is understood about the nuclear contribution above the % melt temperature $(C^{(nuc)}_ν≈3R)$ and how it should transition to the high-temperature limit $(C^{(nuc)}_ν\sim\frac{3}{2}R)$. Here, we describe an algorithm for extracting both the thermal nuclear and thermal electronic contributions from quantum molecular dynamics (QMD) simulations. We then use the VASP QMD package to probe thermal nuclear behavior of liquid aluminum at normal density to compare the results to semi-empirical models – the Johnson generic model, the Chisolm high-temperature liquid model, and the CRIS model. The thermal electronic energy is also calculated from the VASP results and compared to the Kohn-Sham calculations from QE-DFT simulations, Green’s function average atom calculations, and the Thomas-Fermi atomic model.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

A simulation-based model for understanding the time dependent x-ray drive asymmetries and error bars in indirectly driven implosions on the National Ignition Facility

Time-dependent low-mode asymmetries are believed to play a leading role in limiting the performance of current inertial confinement fusion implosions on the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)]. These long wavelength modes are initiated and driven by asymmetries in the x-ray flux from the hohlraum; however, the underlying hydrodynamics of the implosion also act to modify and amplify these asymmetries. Here we present here a simulation-based model connecting the time-dependent drive asymmetry seen by the capsule to the measured inflight and hot spot symmetries. This approach is based on a Green's function analysis for which we evaluate the response of the capsule to impulses of drive asymmetry at a series of times. Our model sheds new light on the sensitivity to the drive asymmetry of an imploded capsule, giving a new tool for design. Inverting the problem and finding the drive asymmetry needed to match the experimental data allow us to tightly constrain the drive asymmetry seen by the capsule, providing an error estimate on the result. Doing so, we are able to point out when and how the complex hohlraum simulations start to deviate from what they should obtain to match the experimental data. Ultimately, we project to use this model to make some experimental recommendations to fix the time-dependent low-mode asymmetry of indirectly driven implosions and identify additional measurements to further constrain the asymmetries with a view to improving target design on the NIF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

An experimental and theoretical study of the C 1s ionization satellites in CH 3 I

We report the C 1s ionization spectrum of CH 3 I has been studied both experimentally and theoretically. Synchrotron radiation has been employed to record polarization dependent photoelectron spectra at a photon energy of 614 eV. These spectra encompass the main-line due to the C 1s single-hole state and the peaks associated with the shake-up satellites. Vertical ionization energies and relative photoelectron intensities have been computed using the fourth-order algebraic-diagrammatic construction approximation scheme for the one-particle Green’s function and the 6-311++G** basis set. The theoretical spectrum derived from these calculations agrees qualitatively with the experimental results, thereby allowing the principal spectral features to be assigned. According to our calculations, two 2 A 1 shake-up states of the C 1s -1 σ CI → σ$*\atop{CI}$ type with singlet and triplet intermediate coupling of the electron spins (S' = 0, 1) play an important role in the spectrum and contribute significantly to the overall intensity. Both of these states are expected to have dissociative diabatic potential energy surfaces with respect to the C–I separation. Whereas the upper of these states perturbs the manifold of Rydberg states, the lower state forms a band which is characterized by a strongly increased width. Our results indicate that the lowest shake-up peak with significant spectral intensity is due to the pair (S' = 0, 1) of 2 E (C 1s -1 I 5p → σ$*\atop{CI}$) states. We predict that these 2 E states acquire photoelectron intensity due to spin-orbit interaction. Lastly, such interactions play an important role here due to the involvement of the I 5p orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

View factor estimation of hot spot velocities in inertial confinement fusion implosions at the National Ignition Facility

nertial confinement fusion (ICF) experiments at the National Ignition Facility (NIF) suffer from asymmetries in thex-ray drive that degrade capsule performance compared to expectations for a symmetric one-dimensional implosion.Mode 1, or pole-to-pole, drive asymmetry can reduce confinement and implosion efficiency, driving a bulk motion ofthe hot spot that is detectable with neutron diagnostics. Understanding and removing sources of mode 1 asymmetry inICF implosions is important for improving performance, and the three-dimensional nature of the problem makes high-resolution radiation-hydrodynamic modeling extremely computationally expensive. This work describes a reducedorder view factor model that calculates the drive asymmetry induced by beam-to-beam variations in laser delivery andhohlraum diagnostic windows along the equator. Capsule response is estimated by coupling to a Green’s function thatrelates final hot spot velocity to the applied time-varying mode 1 asymmetry. The model makes several predictionsabout the impact of mode 1 drivers such as laser delivery and target misalignment, and achieves good agreementin both magnitude and vector direction for several shots in three families of high-performance platforms. However,notable discrepancies suggest other potential sources of mode 1 asymmetry not captured by the model are also at play

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Stochastic evaluation of fourth-order many-body perturbation energies

A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green’s functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n 5.3 ) size-dependence of cost, which is nearly two ranks lower than the O(n 7 ) dependence of the deterministic MP4 algorithm. Furthermore, it evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mE h (1.1% of the total basis-set correlation energy), 38 mE h (2.6%), 110 mE h (5.5%), and 280 mE h (9.0%), respectively, after about 10 9 MC steps.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Flux-driven algebraic damping of m = 2 diocotron mode

Experiments with pure electron plasmas in a Malmberg–Penning trap have observed linear in time, algebraic damping of m = 2 diocotron modes. Transport due to small field asymmetries produces a low-density halo of electrons moving radially outward from the plasma core, and the mode damping begins when the halo reaches the resonant radius of the mode. The damping rate is proportional to the flux of halo particles through the resonant layer. The damping is related to, but distinct from spatial Landau damping in which a linear wave–particle resonance produces exponential damping. This paper reports an analytic theory that captures the main signatures reported for this novel damping, namely, that the damping begins when the halo particles reach the resonant radius and that the damping is algebraic in time with nearly constant damping rate. The model also predicts a nonlinear frequency shift. The model provides two ways to think about the damping. It results from a transfer of canonical angular momentum from the mode to halo particles being swept by the mode field through the nonlinear cat's eye orbits of the resonant region. More mechanistically, the electric field produced by the perturbed charge density of the resonant particles acts back on the plasma core causing E × B drift that gives rise to the damping and nonlinear frequency shift.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Traveling wakefield tube: THz source powered by nonrelativistic electron beam

High peak power, tunable, narrowband terahertz emitters are becoming sought after given their portability, efficiency, and ability to be deployed in the field for industrial, medical, and military applications. The use of accelerator systems producing THz frequencies via Cherenkov radiation, generated by passing an electron beam through a slow-wave wakefield structure, is a promising method to meet future THz requirements. To date, efforts have been dedicated to analysis and design of sources utilizing laser seeded bunched electron beam drivers with relativistic energies beyond 5 MeV. Presented here is a wakefield THz generation scheme based on passing a long quasi-dc nonrelativistic beam (200 keV) through a dielectric loaded travelling wave structure. Reduced energy allows for compactness and portability of the accelerator as the size and weight of the dielectric slow wave structure is vanishingly small compared to the accelerator unit. The presented scheme can serve as a tunable high peak power THz source operated between 0.4-1.6 THz and produces power gain by a factor of five with an average efficiency of 6.8%

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe–Salpeter equation calculations of molecules

The ab initio GW plus Bethe–Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn–Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm–Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn–Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel’s set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.

McKeon, Caroline A. (ORCID:0000000217373503)↗
DOE OSTI2022

Mason–Weaver theory: Revised and extended for a semi-infinite domain

Mason and Weaver developed equations to describe small particles settling under the influence of gravity and Brownian motion, including the limiting case for an infinitely deep suspension. We encountered this common convection–diffusion equation and no-flux boundary conditions in a model for dynamics of adsorbed polymers in dead end pores of a depolymerization catalyst. Close examination reveals that the Mason–Weaver solution is not correct for the infinite domain with a non-uniform initial condition. In this paper, we obtain the time dependent Green’s function for the no flux boundary condition and also for a more general reactive boundary condition. We demonstrate how the results provide solutions, via superposition, which provide solutions for several boundary conditions and all initial conditions.

Chen, Ziqiu↗
DOE OSTI2022

Measurement of amplification and absorption of a THz quantum-cascade metasurface free-space amplifier

An active amplifying metasurface based on a quantum-cascade gain material at 2.7 THz is studied. The metasurface is first evaluated as the active component of an external cavity laser with excellent beam quality and frequency tunability from 2.55–2.8 THz. Amplification and absorption of the metasurface alone are then separately measured at a single frequency using a probe signal from a CO 2 -pumped gas laser operating at 2.743 THz. The metasurface reflectance vs bias is measured and compared with expectations from non-equilibrium Green’s function simulations of the quantum-cascade gain material and FEM simulations of the metasurface reflectance. A peak amplification on the order of 0.3 dB is measured. Design strategies are discussed for increasing single-reflection amplification (upward of 10 dB) and reducing power dissipation. Further increased amplification could be achieved by cascading multiple metasurfaces.

Curwen, Christopher A.↗
DOE OSTI2024

Electric fields near undulating dielectric membranes

Dielectric interfaces are crucial to the behavior of charged membranes, from graphene to synthetic and biological lipid bilayers. Understanding electrolyte behavior near these interfaces remains a challenge, especially in the case of rough dielectric surfaces. A lack of analytical solutions consigns this problem to numerical treatments. Here, we report an analytic method for determining electrostatic potentials near curved dielectric membranes in a two-dimensional periodic “slab” geometry using a periodic summation of Green’s functions. This method is amenable to simulating arbitrary groups of charges near surfaces with two-dimensional deformations. We concentrate on one-dimensional undulations. We show that increasing membrane undulation increases the asymmetry of interfacial charge distributions due to preferential ionic repulsion from troughs. In the limit of thick membranes, we recover results mimicking those for electrolytes near a single interface. Our work demonstrates that rough surfaces generate charge patterns in electrolytes of charged molecules or mixed-valence ions.

Chemistry↗
DOE OSTI2024

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗
DOE OSTI2025

Renormalization of states and quasiparticles in many-body downfolding

We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We show that the renormalization factor provides a unique measure of the quality of the compression as it directly represents the projection between the approximate stationary state of the many-body Hamiltonian and the full many-body wavefunction. Hence, the renormalization factor is a measure of fidelity between the effective (reduced-rank) description and the full many-body treatment for arbitrary (i.e., ground and excited) states. When the entire problem is mapped on a system of interacting quasiparticles [Romanova et al., npj Comput. Mater. 9, 126 (2023)], the effective Hamiltonians can faithfully reproduce the physics only when a clear energy scale separation exists between the subsystems and their environment. We also demonstrate that it is necessary to include quasiparticle renormalization at distinct energy scales, capturing the distinct interaction between subsystems and their surrounding environments. Numerical results from simple, exactly solvable models highlight the limitations and strengths of this approach, particularly for ground and low-lying excited states. This work lays the groundwork for applying dynamical downfolding techniques to problems concerned with (quantum) interfaces.

Green-functions technique↗
DOE OSTI2015

Full self-consistency versus quasiparticle self-consistency in diagrammatic approaches: Exactly solvable two-site Hubbard model

Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ₁ from the first-order perturbation theory, and the exact vertex Γ E ). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. Results obtained with the exact vertex are directly related to the present open question—which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on Perturbation Theory systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗