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Results for “numeric invariants”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems

We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. Here, we also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Shadow of complex fixed point: Approximate conformality of Q > 4 Potts model

We study the famous example of weakly first-order phase transitions in the (1 + 1)-dimensional quantum Q-state Potts model with Q > 4. We numerically show that these weakly first-order transitions have approximately conformal invariance. Specifically, we find that entanglement entropy on considerably large system sizes fits perfectly with the universal scaling law of this quantity in conformal field theories (CFTs). This supports that the weakly first-order transitions are proximate to complex fixed points, which are described by recent conjectured complex CFTs. Moreover, the central charge extracted from this fitting is close to the real part of the complex central charge of these complex CFTs. Furthermore, we also study the conformal towers and the drifting behaviors of these conformal data (e.g., central charge and scaling dimensions).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Probing the Holomorphic Anomaly of the D = 2, N = 2, Wess–Zumino Model on the Lattice

We study a generalization of the Langevin equation, that describes fluctuations, of commuting degrees of freedom, for scalar field theories with worldvolumes of arbitrary dimension, following Parisi and Sourlas and correspondingly generalizes the Nicolai map. Supersymmetry appears inevitably, as defining the consistent closure of system + fluctuations and it can be probed by the identities satisfied by the correlation functions of the noise fields, sampled by the action of the commuting fields. This can be done effectively, through numerical simulations. We focus on the case where the target space is invariant under global rotations, in Euclidian signature, corresponding to global Lorentz transformations, in Lorentzian signature. This can describe target space supersymmetry. In this case a cross-term, that is a total derivative for abelian isometries, or when the fields are holomorphic functions of their arguments, can lead to obstructions. We study its effects and find that, in two dimensions, it cannot lead to the appearance of the holomorphic anomaly, in any event, when fluctuations are taken into account, because continuous symmetries can’t be broken in two dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Evaluating one-loop string amplitudes

We evaluate one-loop open-string amplitudes at finite \alpha' α ′ for the first time. Our method involves a deformation of the integration contour over the modular parameter \tau τ to a fractal contour introduced by Rademacher in the context of analytic number theory. This procedure leads to explicit and practical formulas for the one-loop four-point amplitudes in type-I superstring theory, amenable to numerical evaluation. We plot the amplitudes as a function of the Mandelstam invariants s s and t t and directly verify long-standing conjectures about their behaviour at high energies.

Eberhardt, Lorenz↗
NASA NTRS1975

ORACLS - A modern control theory design package

A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.

Armstrong, E. S.↗
NASA NTRS1990

Stochastic robustness of linear control systems

A simple numerical procedure for estimating the stochastic robustness of a linear, time-invariant system is described. Monte Carlo evaluation of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This definition of robustness is an alternative to existing deterministic definitions that address both structured and unstructured parameter variations directly. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variations. Trivial extensions of the procedure admit alternate discriminants to be considered. Thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions also can be estimated. Results are particularly amenable to graphical presentation.

Stengel, Robert F.↗
NASA NTRS1990

A first-order Lyapunov robustness method for linear systems with uncertain parameters

A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.

Leal, M. A.↗
NASA NTRS2003

Computational Aeroacoustics: An Overview

An overview of recent advances in computational aeroacoustics (CAA) is presented. CAA algorithms must not be dispersive and dissipative. It should propagate waves supported by the Euler equations with the correct group velocities. Computation domains are inevitably finite in size. To avoid the reflection of acoustic and other outgoing waves at the boundaries of the computation domain, it is required that special boundary conditions be imposed at the boundary region. These boundary conditions either absorb all the outgoing waves without reflection or allow the waves to exit smoothly. High-order schemes, invariably, supports spurious short waves. These spurious waves tend to pollute the numerical solution. They must be selectively damped or filtered out. All these issues and relevant computation methods are briefly reviewed. Jet screech tones are known to have caused structural fatigue in military combat aircrafts. Numerical simulation of the jet screech phenomenon is presented as an example of a successful application of CAA.

Tam, Christopher K. W.↗
NASA NTRS2004

Verification of Java Programs using Symbolic Execution and Invariant Generation

Software verification is recognized as an important and difficult problem. We present a norel framework, based on symbolic execution, for the automated verification of software. The framework uses annotations in the form of method specifications an3 loop invariants. We present a novel iterative technique that uses invariant strengthening and approximation for discovering these loop invariants automatically. The technique handles different types of data (e.g. boolean and numeric constraints, dynamically allocated structures and arrays) and it allows for checking universally quantified formulas. Our framework is built on top of the Java PathFinder model checking toolset and it was used for the verification of several non-trivial Java programs.

Pasareanu, Corina↗
DOE OSTI2026

Optimal invariant sets for atomistic machine learning

The representation of atomic configurations for machine learning models has led to numerous sets of descriptors. However, many descriptor sets are incomplete and/or functionally dependent. Incomplete sets cannot faithfully represent atomic environments. Yet complete constructions often suffer from a high degree of functional dependence, where some descriptors are functions of others. These redundant descriptors do not improve discrimination between atomic environments. We employ pattern recognition techniques to remove dependent descriptors to produce the smallest possible set that satisfies completeness. We apply this in two ways: First, we refine an existing description, the atomic cluster expansion. Second, we augment an incomplete construction, yielding a new message-passing neural network architecture that can recognize up to 5-body patterns. This architecture shows strong accuracy on state-of-the-art benchmarks while retaining low computational cost. Our results demonstrate the utility of this strategy to optimize descriptor sets across a range of descriptors and application datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Spectral method for a kinetic swarming model

Here we present the first numerical method for a kinetic description of the Vicsek swarming model. The kinetic model poses a unique challenge, as there is a distribution dependent collision invariant to satisfy when computing the interaction term. We use a spectral representation linked with a discrete constrained optimization to compute these interactions. To test the numerical scheme we investigate the kinetic model at different scales and compare the solution with the microscopic and macroscopic descriptions of the Vicsek model. Lastly, we observe that the kinetic model captures key features such as vortex formation and traveling waves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A cornucopia of AdS5 vacua

We report on a systematic search for AdS 5 vacua corresponding to critical points of the potential in the five-dimensional $$ \mathcal{N} $$ N = 8 SO(6) gauged supergravity. By employing Google’s TensorFlow Machine Learning library, we find the total of 32 critical points including 5 previously known ones. All 27 new critical points are non-supersymmetric. We compute the mass spectra of scalar fluctuatons for all points and find that the non- supersymmetric AdS 5 vacua are perturbatively unstable. Many of the new critical points can be found analytically within consistent truncations of the $$ \mathcal{N} $$ N = 8 supergravity with respect to discrete subgroups of the S(O(6) × GL(2 , R)) symmetry of the potential. In par- ticular, we discuss in detail a $$ {\mathrm{\mathbb{Z}}}_2^3 $$ Z 2 3 -invariant truncation with 10 scalar fields and 15 critical points. We also compute explicitly the scalar potential in a $$ {\mathrm{\mathbb{Z}}}_2^2 $$ Z 2 2 -invariant extension of that truncation to 18 scalar fields and reproduce 17 of the 32 critical points from the numerical search. Finally, we show that the full potential as a function of 42 scalar fields can be studied analytically using the so-called solvable parametrization. In particular, we find that all critical points lie in a Z 2 -invariant subspace spanned by 22 scalar fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A dynamical polynomial chaos approach for long-time evolution of SPDEs

We propose a Dynamical generalized Polynomial Chaos (DgPC) method to solve time-dependent stochastic partial differential equations (SPDEs) with white noise forcing. The long-time simulation of SPDE solutions by Polynomial Chaos (PC) methods is notoriously difficult as the dimension of the stochastic variables increases linearly with time. Exploiting the Markovian property of white noise, DgPC implements a restart procedure that allows us to expand solutions at future times in terms of orthogonal polynomials of the measure describing the solution at a given time and the future white noise. The dimension of the representation is kept minimal by application of a Karhunen–Loeve (KL) expansion. Using frequent restarts and low degree polynomials on sparse multi-index sets, the method allows us to perform long time simulations, including the calculation of invariant measures for systems which possess one. We apply the method to the numerical simulation of stochastic Burgers and Navier–Stokes equations with white noise forcing. Our method also allows us to incorporate time-independent random coefficients such as a random viscosity. We propose several numerical simulations and show that the algorithm compares favorably with standard Monte Carlo methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Full-dimensional quantum calculations of vibrational levels of NH 4 + and isotopomers on an accurate ab initio potential energy surface

Vibrational energy levels of the ammonium cation (NH 4 + ) and its deuterated isotopomers are calculated using a numerically exact kinetic energy operator on a recently developed nine-dimensional permutation invariant semiglobal potential energy surface fitted to a large number of high-level ab initio points. Like CH4, the vibrational levels of NH 4 + and ND 4 + exhibit a polyad structure, characterized by a collective quantum number P = 2(v 1 + v 3 ) + v 2 + v 4 . As a result, the low-lying vibrational levels of all isotopomers are assigned and the agreement with available experimental data is better than 1 cm –1 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Topological solitonic macromolecules

Being ubiquitous, solitons have particle-like properties, exhibiting behaviour often associated with atoms. Bound solitons emulate dynamics of molecules, though solitonic analogues of polymeric materials have not been considered yet. Here we experimentally create and model soliton polymers, which we call “polyskyrmionomers”, built of atom-like individual solitons characterized by the topological invariant representing the skyrmion number. With the help of nonlinear optical imaging and numerical modelling based on minimizing the free energy, we reveal how topological point defects bind the solitonic quasi-atoms into polyskyrmionomers, featuring linear, branched, and other macromolecule-resembling architectures, as well as allowing for encoding data by spatial distributions of the skyrmion number. Application of oscillating electric fields activates diverse modes of locomotion and internal vibrations of these self-assembled soliton structures, which depend on symmetry of the solitonic macromolecules. Our findings suggest new designs of soliton meta matter, with a potential for the use in fundamental research and technology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Effects of electron inertia in collisionless magnetic reconnection

We present a study of collisionless magnetic reconnection within the framework of full two-fluid MHD for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure and electron inertia. We performed 2.5D simulations using a pseudo-spectral code with no dissipative effects. We check that the ideal invariants of the problem are conserved down to round-off errors. Our numerical results confirm that the change in the topology of the magnetic field lines is exclusively due to the presence of electron inertia. The computed reconnection rates remain a fair fraction of the Alfvén velocity, which therefore qualifies as fast reconnection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

I-ball formation with logarithmic potential

A coherently oscillating real scalar field with potential shallower than quadratic one fragments into spherical objects called I-balls. We study the I-ball formation for logarithmic potential which appears in many cosmological models. We perform lattice simulations and find that the I-balls are formed when the potential becomes dominated by the quadratic term. Furthermore, we estimate the I-ball profile assuming that the adiabatic invariant is conserved during formation and obtain the result that agrees to the numerical simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Basis light-front quantization for a chiral nucleon-pion Lagrangian

We present the first application of the basis light-front quantization method to a simple chiral model of the nucleon-pion system as a relativistic bound state for the physical proton. In this work, the light-front mass-squared matrix of the nucleon-pion system is obtained within a truncated basis. The mass and the corresponding light-front wave function (LFWF) of the proton are computed by numerical diagonalization of the resulting mass-squared matrix. With the boost-invariant LFWF, we calculate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗