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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Dependence of nuclear quadrupole resonance transitions on the electric field gradient asymmetry parameter for nuclides with half-integer spins

Allowed transition energies and eigenstate expansions have been calculated and tabulated in numerical form as functions of the electric field gradient asymmetry parameter for the zero field Hamiltonian of quadrupolar nuclides with I=3/2,5/2,7/2, and 9/2. These results are essential to interpret nuclear quadrupole resonance (NQR) spectra and extract accurate values of the electric field gradient tensors. Applications of NQR methods to studies of electronic structure in heavy element systems are proposed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Surrogate model for third-integer resonance extraction at the Fermilab Delivery Ring

We present an ongoing work in which a surrogate model is being developed to reproduce the response dynamics of the third-integer resonant extraction process in the Delivery Ring (DR) at Fermilab. This is in pursuit of smoothly extracting circulating beam to the Mu2e Experiment’s production target, whereby the goal is to extract a uniform slice of the circulating 1e12 protons in the DR over 25,000 turns (43 ms). The DR contains 3 harmonic sextupoles that excite a third-integer resonance and three fast, tune-ramping quadrupole magnets that drive the horizontal tune towards the 29/3 resonance. In our initial work, the surrogate model trains on a semi-analytical simulation provided in the same format as live data. Using Reinforcement Learning (and other potential ML methods), the trained surrogate acts as the “environment” in which a simple ML control agent could learn to dynamically adjust the quadrupole ramp at 430 break points within the 43 microsecond spill window. The controller will be hosted on a dedicated Arria 10 FPGA. In this work, we report the accuracy and fidelity of the surrogate model in comparison to the response dynamics of the physics simulator.

Narayanan, Aakaash [Fermilab]↗
DOE OSTI2022

Sequential linear integer programming for integer optimal control with total variation regularization

We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Decomposing the Train-Scheduling Problem into Integer-Optimal Polytopes

This paper presents conditions for which the linear relaxation for the train-scheduling problem is integer optimal. These conditions are then used to identify how to partition a general problem’s feasible region into integer-optimal polytopes. Such an approach yields an extended formulation that contains far fewer binary variables. Our computational experiments show that this approach results in significant computational savings. Moreover, this approach scales well when the train-scheduling problem is modeled using smaller time increments, allowing for higher fidelity models to be solved without significantly increasing the required computational time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Integer versus half-integer spin on an approximate honeycomb lattice

Recent interest in honeycomb lattice materials has focused on their potential to host quantum spin liquid (QSL) states. Variations in bond angles and spin allow a range of interesting behaviors on this lattice, from the predicted QSL ground state of the Kitaev model to exotic magnetic orders. Here we report the physical properties of two compounds with rare earths on an approximate honeycomb lattice. Here, the isostructural compounds Nd 2 S 5 Sn (J = 9/2) and Pr 2 S 5 Sn (J = 4) permit a direct comparison of half-integer versus integer spins on this lattice. We find strikingly different magnetic properties for the two compounds. Nd 2 S 5 Sn orders antiferromagnetically at T N ≈ 2.5 K and undergoes several magnetic transitions to other ordered states under applied field. Pr 2 S 5 Sn displays no magnetic ordering transition above T = 0.41 K, and may be proximate to a spin liquid state.

36 MATERIALS SCIENCE↗
DOE OSTI2020

On Mixed-Integer Programming Formulations for the Unit Commitment Problem

We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved—and in the process, we identify a new state-of-the-art UC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Quantum Oscillations at Integer and Fractional Landau Level Indices in Single-Crystalline ZrTe 5

A three-dimensional (3D) Dirac semimetal (DS) is an analogue of graphene, but with linear energy dispersion in all (three) momentum directions. 3D DSs have been a fertile playground in discovering novel quantum particles, for example Weyl fermions, in solid state systems. Many 3D DSs were theoretically predicted and experimentally confirmed. Here, we report here the results in exfoliated ZrTe 5 thin flakes from the studies of aberration-corrected scanning transmission electron microscopy and low temperature magneto-transport measurements. We observed several unique results. First, a π Berry phase was obtained from the Landau fan diagram of the Shubnikov-de Haas oscillations in the longitudinal conductivity σ xx . Second, the longitudinal resistivity ρ xx shows a linear magnetic field dependence in the quantum limit regime. Most surprisingly, quantum oscillations were also observed at fractional Landau level indices N = 5/3 and 7/5, demonstrating strong electron-electron interaction effects in ZrTe 5 .

36 MATERIALS SCIENCE↗
DOE OSTI2023

Incremental Interval Assignment by Integer Linear Algebra with Improvements

Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. Here we add vectors from the nullspace to improve the initial solution, maintaining Ax = b Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Quantum Integers

In number theory, a partition of a positive integer n is a way of writing n as a sum of positive integers. The number of partitions of n is given by the partition function p(n). Inspired by quantum information processing, we extend the concept of partitions in number theory as follows: for an integer n, we treat each partition as a basis state of a quantum system representing that number n, so that the Hilbert-space that corresponds to that integer n is of dimension p(n); the 'classical integer' n can thus be generalized into a (pure) quantum state ||psi(n) > which is a superposition of the partitions of n, in the same way that a quantum bit (qubit) is a generalization of a classical bit. More generally, rho(n) is a density matrix in that same Hilbert-space (a probability distribution over pure states). Inspired by the notion of quantum numbers in quantum theory (such as in Bohr's model of the atom), we then try to go beyond the partitions, by defining (via recursion) the notion of 'sub-partitions' in number theory. Combining the two notions mentioned above, sub-partitions and quantum integers, we finally provide an alternative definition of the quantum integers [the pure-state |psi'(n)> and the mixed-state rho'(n),] this time using the sub-partitions as the basis states instead of the partitions, for describing the quantum number that corresponds to the integer n.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Anisotropic fractal media by vector calculus in non-integer dimensional space

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Quantum Circuit Designs of Integer Division Optimizing T-Count and T-Depth

Quantum circuits for basic mathematical functions such as division are required to implement scientific computing algorithms on quantum computers. In this work, we propose two designs for quantum integer division. The designs are based on quantum Clifford+T gates and are optimized for T-count and T-depth. Quantum circuits that are based on Clifford+T gates can be made fault tolerant in nature but the T gate is very costly to implement. As a result, reducing T-count and T-depth have become important optimization goals. Existing quantum hardware is limited in terms of number of available qubits. Thus, ancillary qubits are a circuit overhead that needs to be kept to a minimum. We propose two quantum integer division circuits. The first quantum integer division circuit is based on the non-restoring division algorithm. The proposed non-restoring division circuit is optimized for total quantum hardware (T-count and T-depth) cost but requires 2* n + 1 ancillary qubits. We also propose a quantum integer division circuit based on the restoring division algorithm. The proposed restoring division circuit is optimized for total qubits. The design requires only n ancillary qubits but will need more quantum hardware than the non-restoring division circuit. Both proposed quantum circuits are based on (i) a new quantum conditional addition circuit, (ii) a new quantum adder-subtractor and (iii) a new quantum subtraction circuit. Further, both designs are compared and shown to be superior to existing work in terms of T-count and T-depth. The proposed quantum non-restoring integer division circuit has a 96% improvement in terms of T-count and a 93% improvement in terms of T-depth compared to existing work. The proposed quantum restoring integer division circuit has a 91% improvement in terms of T-count and a 86% improvement in terms of T-count compared to the existing work.

Thapliyal, Himanshu↗
DOE OSTI2019

A Multi-Parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems

Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. Herein, we present novel algorithms for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-parametric programming theory, the main idea is to recast the lower level problem as a multi-parametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems.

42 ENGINEERING↗