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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Fixed points in three dimensions described by conformal field theories with \ensuremath{M N}_{m,n} = O(m)^n\rtimes S_n M N m , n = O ( m ) n ⋊ S n global symmetry have extensive applications in critical phenomena. Associated experimental data for m=n=2 m = n = 2 suggest the existence of two non-trivial fixed points, while the \varepsilon ε expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters m m and n n , with critical exponents in good agreement with experimental determinations in the m=n=2 m = n = 2 case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters m m and n n . We find that one family of kinks approaches a perturbative limit as m m increases, and using large spin perturbation theory we construct a large m m expansion that fits well with the numerical data. This new expansion, akin to the large N N expansion of critical O(N) O ( N ) models, is compatible with the fixed point found in the \varepsilon ε expansion. For the other family of kinks, we find that it persists only for n=2 n = 2 , where for large m m it approaches a non-perturbative limit with \Delta_\phi\approx 0.75 Δ ϕ ≈ 0.75 . We investigate the spectrum in the case \ensuremath{M N}_{100,2} M N 100 , 2 and find consistency with expectations from the lightcone bootstrap.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Spontaneous breaking of finite group symmetries at all temperatures

We study conformal field theories with finite group symmetries with spontaneous symmetry breaking (SSB) phases which persist at all temperatures. We work with two \lambda \phi^4 λ ϕ 4 theories coupled through their mass terms. The two \lambda \phi^4 λ ϕ 4 theories are chosen to preserve either the cubic symmetry group, or the tetrahedral symmetry group. A one-loop calculation in the 4-\epsilon 4 − ϵ expansion shows that there exist infinitely many fixed points that can host an all temperature SSB phase. An analysis of the renormalization group (RG) stability matrix of these fixed points, reveals that their spectrum contains at least three relevant operators. In other words, these fixed points are tetracritical points.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Fast explicit solutions for neutrino-electron scattering: Explicit asymptotic methods

Here, we present results of explicit asymptotic approximations applied to neutrino-electron scattering in a representative model of neutrino population evolution under conditions characteristic of core-collapse supernova explosions or binary neutron star mergers. It is shown that this approach provides stable solutions of these stiff systems of equations, with accuracy and time stepping comparable to that for standard implicit treatments such as backward Euler, fixed point iteration, and Anderson-accelerated fixed point iteration. Because each time step can be computed more rapidly with the explicit asymptotic approximation than with implicit methods, this suggests that algebraically stabilized explicit integration methods could be used to compute neutrino evolution coupled to hydrodynamics more efficiently in stellar explosions and mergers than the methods currently in use.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Stability analysis of a one-dimensional multiphysics model of a molten salt fast reactor

Reactor designs with a fast neutron spectrum have recently moved into the research focus for possible Generation IV reactor concepts - a representative of which is the molten salt fast reactor (MSFR). In order to assess the safety and reliability of this reactor concept, it is necessary to obtain knowledge of the system behaviour. An important part of this research concerns the dynamical stability of the MSFR. Research regarding the MSFR stability so far has either been using linearized models for stability criteria or only been examining certain transients at fixed parameter values. This work delivers a comprehensive stability analysis for a non-linearized MSFR model, and a wide range of values for all relevant parameters. For this purpose, a one-dimensional MSFR model was set up, taking neutron kinetics and thermal hydraulics in the form of a system of differential equations into account. The stability of this model was investigated by means of the numerical tool MATCONT, which was used to monitor the evolution of a so-called fixed-point solution, here referring to the steady state at operating conditions of the system, while system parameters got varied. The MATCONT analyses showed no loss of stability for any of the considered parameter variations and no solutions that might co-exist in parallel with the steady-state fixed-point solution. Therefore these results indicate a stable fixed point to which all solution transients converge, making the considered MSFR model insusceptible to deviations from the equilibrium. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Modal dynamics of high-frequency transverse combustion instabilities

This paper investigates the modal dynamics of self-excited high frequency transverse instabilities in a multi-nozzle, swirl-stabilized can combustor. It utilizes results from multiple pressure sensors to decompose the disturbance into clockwise (CW) and counter-clockwise (CCW) waves, enabling a reconstruction of the pressure amplitude, phase, anti-nodal line location, and spin ratio. While these types of decompositions have been demonstrated on small scale combustors, particularly annular combustors, this is the first study to analyze these results for a high power, multi-nozzle can combustor. Its particular focus is in characterizing the system evolution in phase space and the nature of the system attractors under linearly unstable conditions; results are presented in spin ratio-phase difference space, so that limit cycle oscillations appear as fixed points. Results are shown for conditions where three different attractors dominate (standing, CW, and CCW) but are taken for very long time periods (~50,000 cycles) so that the system's interaction with these attractors can be observed. For the standing mode-dominated case, the phase portrait shows spiral trajectories converging to a single fixed point. For the spinning mode dominated cases, however, multiple fixed points and saddle points were observed, and the trajectories showed a more complicated structure. It was also shown that even though the CW mode is dominant, this mode intermittently switches to standing or CCW modes for short period. These results suggest that the strength of each attractor depends on test conditions and that random noise stochastically perturbs the system so that large regions of the phase space are explored. Lastly, one interesting observation is that the angular velocity of the anti-nodal line linearly varies with the spin ratio under standing-mode dominant conditions.

42 ENGINEERING↗
DOE OSTI2023

Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low-rank approximation of the dielectric matrix

We present an efficient preconditioning technique for accelerating the fixed-point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low-rank approximation of the dielectric matrix (LRDM) based on Gâteaux derivatives of the residual of fixed-point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these Gâteaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous self-consistent field iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from ~100 to 1100 atoms (~500–20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized d orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20–30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed-point iteration in some cases. Lastly, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4-fold reduction in computational cost for the total ground-state calculation compared to other preconditioners.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.

Serrallés, José Cruz [Weill Cornell Med. Coll.]↗
DOE OSTI2021

Non-Wilsonian ultraviolet completion via transseries

We study some of the implications for the perturbative renormalization program when augmented with the Borel–Ecalle resummation. We show the emergence of a new kind of nonperturbative fixed point for the scalar [Formula: see text] model, representing an ultraviolet self-completion by transseries. We argue that this completion is purely non-Wilsonian and it depends on one arbitrary constant stemming from the transseries solution of the renormalization group equation. On the other hand, if no fixed points are demanded through the adjustment of this arbitrary constant, we end up with an effective theory in which the scalar mass is quadratically-sensitive to the cutoff, even working in dimensional regularization. Complete decoupling of the scalar mass to this energy scale can be used to determine a physical prescription for the Borel–Laplace resummation of the renormalons in nonasymptotically free models. We also comment on possible orthogonal scenarios available in the literature that might play a role when no fixed points exist.

Physics↗
DOE OSTI2021

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Anderson acceleration with approximate calculations: Applications to scientific computing

Here we provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least-squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed-point iterations arising from the Richardson's scheme to solve linear systems with open-source benchmark matrices with various preconditioners and (ii) non-linear deterministic fixed-point iterations arising from non-linear time-dependent Boltzmann equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Projective embedding of dynamical systems: Uniform mean field equations

Herein we study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the original system dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of rank-1 projector operator, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. We prove a variety of results on the relationship between the spectrum of the Jacobian for fixed points in the original and in the embedded system. Direct applications of PEDS can be non-convex optimization and machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Finite-size effects in periodic coupled cluster calculations

Here, we provide the first rigorous study of the finite-size error in the simplest and representative coupled cluster theory, namely the coupled cluster doubles (CCD) theory, for gapped periodic systems. Given exact Hartree-Fock orbitals and their corresponding orbital energies, we demonstrate that the correlation energy obtained from the approximate CCD method, after a finite number of fixed-point iterations over the amplitude equation, exhibits a finite-size error scaling as $\mathcal{O}(N^{-\frac{1}{3}}_k)$. Here $N_k$ is the number of discretization points in the Brillouin zone and characterizes the system size. Under additional assumptions ensuring the convergence of the fixed-point iterations, we demonstrate that the CCD correlation energy also exhibits a finite-size error scaling as $\mathcal{O}(N^{-\frac{1}{3}}_k)$. Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculation can be boosted to $\mathcal{O}(N^{-1}_k)$ with accurate amplitudes. This also provides the first proof of the scaling of the finite-size error in the third order Møller-Plesset perturbation theory (MP3) for periodic systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

High-electric-field behavior of the metal-insulator transition in TiS3 nanowire transistors

We investigate the behavior of the metal-insulator transition (MIT) in TiS 3 nanowire field-effect transistors, in the strongly nonequilibrium limit that has, thus far, largely been neglected. Under high electric fields within the TiS 3 channel (≤115 kV/cm), we observe the emergence of a critical fixed point, separating insulating and metallic regions in the transfer curves of the device. The critical gate voltage that defines this fixed point evolves systematically with the drain bias (field), allowing us to map out a phase diagram that identifies the conditions for metallicity or for insulating behavior. Dependent upon the choice of the gate voltage used to tune the carrier concentration in the nanowire, the existence of the field-induced MIT allows the TiS 3 to be either insulating or metallic over an extensive range of temperature. The possible connection of this strongly nonequilibrium state to some form of charge density wave is discussed.

2D materials↗
DOE OSTI2020

Dynamical quantum phase transitions of quantum spin chains with a Loschmidt-rate critical exponent equal to $\frac{1}{2}$

In this work, we describe a new universality class of dynamical quantum phase transitions of the Loschmidt amplitude of quantum spin chains off equilibrium criticality. We demonstrate that in many cases it is possible to change the conventional linear singularity of the Loschmidt rate function into a smooth peak by tuning one parameter of the quench protocol. Exactly at the point when this change-over occurs, the singularity of the Loschmidt rate function persists, with a critical exponent equal to $\frac{1}{2}$. The nonequilibrium renormalization group fixed point controlling this universality class is described. An asymptotically exact renormalization group recursion relation is derived around this fixed point to obtain the critical exponent.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Global flow structure and exact formal transseries of the Gubser flow in kinetic theory

In this work we introduce the generic conditions for the existence of a non-equilibrium attractor that is an invariant manifold determined by the long-wavelength modes of the physical system. We investigate the topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the Boltzmann equation by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow and determine all the possible flow lines connecting any pair of UV/IR fixed points. The formal transseries solutions to the Gubser dynamical system around the early-time (UV) and late-time (IR) fixed points are constructed and analyzed. It is proven that these solutions are purely perturbative (or power-law asymptotic) series with a finite radius of convergence. Based on these analyses, we find that Gubser-like expanding kinetic systems do not hydrodynamize owing to the failure of the hydrodynamization process which heavily relies on the classification of (non)hydrodynamic modes in the IR regime. This is in contrast to longitudinal boost-invariant plasmas where the asymptotic dynamics is described by a few terms of the hydrodynamic gradient expansion. We finally compare our results for both Bjorken and Gubser conformal kinetic models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n) O ( m ) × O ( n ) global symmetry in d=3 d = 3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-d ε = 4 − d and in 1/n 1 / n , with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n) O ( 2 ) × O ( n ) theories for various values of n n . Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilon ε and large- n n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Loop current fluctuations and quantum critical transport

We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the “Hertz-Millis” type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving N N species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, \sigma(\omega>0)\sim\omega^{-2/z} σ ( ω > 0 ) ∼ ω − 2 / z , where z z is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large N N expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical N = 1 N = 1 system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, \sigma(\omega>0) \sim \omega^{-2(z-2)/z} σ ( ω > 0 ) ∼ ω − 2 ( z − 2 ) / z , in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Monitored Fluctuating Hydrodynamics

We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes—i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced “sharpening” phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known “charge-fuzzy phase” for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with nontrivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record.

classical statistical mechanics↗