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DOE OSTI2018

Algebraic multigrid for directed graph Laplacian linear systems (NS‐LAMG)

Summary We propose nonsymmetric lean algebraic multigrid (NS‐LAMG), a new algebraic multigrid algorithm for directed graph Laplacian systems that combines ideas from undirected graph Laplacian multigrid solvers and multigrid algorithms for Markov chain stationary distribution systems. Low‐degree elimination, proposed in LAMG for undirected graphs, is generalized to directed graphs and is a key component of NS‐LAMG. In the setup phase, we propose a simple stationary‐aggregation multigrid algorithms for Markov chain stationary distribution systems solver enhanced by low‐degree elimination to find the right null‐space vector that is used for the intergrid transfer operators. Numerical results show that low‐degree elimination improves performance and that NS‐LAMG outperforms generalized minimal residual method with restart and stable bi‐conjugate gradient method for real‐world, directed graph Laplacian linear systems.

Fox, Alyson↗

DOE OSTI2021

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Linear viscoelastic characterization of electrically conductive adhesives used as interconnect in photovoltaic modules

Electrically conductive adhesives (ECAs) are incorporated into recent designs of photovoltaic (PV) modules and replace the traditional metallic solders as interconnects. This transition depicts a significant material change, and a proper understanding of the interconnects' mechanical response has not yet been established. However, such an understanding is necessary to (a) identify the driving forces for module degradation and failure, (b) allow for module design optimization, and (c) enable accurate lifetime predictions. This study summarizes the framework for the mechanical materials characterization and modeling of ECAs for PV applications. Only high-fidelity material models are able to capture the rate and temperature dependency of the ECA interconnect and allow for accurate modeling of the materials response. Furthermore, a linear viscoelastic representation is found to describe the mechanical response of the ECAs sufficiently well. The effects of curing conditions and environmental exposure are investigated, and material models for a variety of ECAs are reported and prepared for the use in numerical simulations. Overall, a finite element simulation of a generic submodel of a shingled cell module is used to highlight the need for high-fidelity material models and demonstrates the error made in the predicted stress states by using less sophisticated models.

14 SOLAR ENERGY↗

DOE OSTI2019

Synthesis and characterization of polylactide-PAMAM “Janus-type” linear-dendritic hybrids

In this report, we introduce a facile and comprehensive synthetic methodology for the preparation of polyester-polyamidoamine (PAMAM) (i.e., polyester: polylactide [PLA] (hydrophobic) and polyamidoamine, PAMAM [hydrophilic]) polymers. A library of PLA-PAMAM linear dendritic block copolymers (LDBCs) in which both l and d, l polylactide were employed in mass ratios of 30:70, 50:50, 70:30, and 90:10 (PLA:PAMAM) were synthesized and analyzed. When placed in aqueous media, the immiscibility of the hydrophilic and hydrophobic segments leads to nanophase-segregation exhibited as the formation of aggregates (e.g., vesicles, worms, and/or micelles). By employing both stereochemical configurations of PLA, the differentiation in mass ratios of PLA-PAMAM aided in elucidating the structure–property relationships of the LDBC system and provided a means toward the control of nanoparticle morphology. Transmission electron microscopy and dynamic light scattering afford the size and shape of the nanoparticles with diameters ranging from 10.6 for low mass ratios to 122.4 nm for high mass ratios of PLA-PAMAM and positive zeta-potential values between +24 mV and +48.2 mV. Moreover, small-angle X-ray scattering (SAXS) studies were employed to obtain more detailed information on the morphological assemblies constructed via direct dissolution. Such insights provide a pathway toward nanomaterials with unique morphologies and tunable properties deemed relevant in the development of next generation biomaterials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Sequential Separation of Linear, Mono–, and Di–Branched Hexane Isomers on a Robust Coordination Polymer with Nonbonding Flexibility

Efficient separation of hexane isomers is a crucial process for upgrading gasoline. Herein, the sequential separation of linear, mono-, and di-branched hexane isomers by a robust stacked 1D coordination polymer termed as Mn-dhbq ([Mn(dhbq)(H 2 O) 2 ], H 2 dhbq = 2,5-dihydroxy-1,4-benzoquinone) is reported. The interchain space of the activated polymer is of optimal aperture size (5.58 Å) that could exclude 2,3-dimethylbutane, while the chain structure can discriminate n-hexane with high capacity (1.53 mmol g –1 at 393 K, 6.67 kPa) by high-density open metal sites (5.18 mmol g –1 ). With the temperature- and adsorbate-dependent swelling of interchain spaces, the affinity between 3-methylpentane and Mn-dhbq can be deliberately controlled from sorption to exclusion, and thus a complete separation of ternary mixture can be achieved. Column breakthrough experiments confirm the excellent separation performance of Mn-dhbq. Furthermore, the ultrahigh stability and easy scalability further highlight the application prospect of Mn-dhbq for separation of hexane isomers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Linear Dichroism of the Optical Properties of SnS and SnSe Van der Waals Crystals

Abstract Tin monochalcogenides SnS and SnSe, belonging to a family of Van der Waals crystals isoelectronic to black phosphorus, are known as environmentally friendly materials promising for thermoelectric conversion applications. However, they exhibit other desired functionalities, such as intrinsic linear dichroism of the optical and electronic properties originating from strongly anisotropic orthorhombic crystal structures. This property makes them perfect candidates for polarization‐sensitive photodetectors working in near‐infrared spectral range. A comprehensive study of the SnS and SnSe crystals is presented, performed by means of optical spectroscopy and photoemission spectroscopy, supported by ab initio calculations. The studies reveal the high sensitivity of the optical response of both materials to the incident light polarization, which is interpreted in terms of the electronic band dispersion and orbital composition of the electronic bands, dictating the selection rules. From the photoemission investigation the ionization potential, electron affinity and work function are determined, which are parameters crucial for the design of devices based on semiconductor heterostructures.

Chemistry↗

DOE OSTI2015

Linear starch and hexanoic acid complexation evaluated by isothermal titration calorimetry

Linear starch form inclusion complexes with fatty acids through hydrophobic interaction. The complexation between starch and fatty acid is affected by many factors, such as starch degree of polymerization (DP), fatty acid structure, and complexation conditions. There is limited information on the use of isothermal titration calorimetry (ITC) in understanding starch‐fatty acid interactions. The effects of temperature and concentration of hexanoic acid on the complexation of debranched waxy maize starch and potato amylose were investigated using ITC. The starch samples were characterized for their molecular size distribution and iodine affinity. Potato amylose and debranched waxy maize starch displayed a major peak DP of 330 and 25, and iodine affinity of 2.9 and 13.9, respectively. The ITC titration data were fitted best to a one set of binding site model. Complexation was exothermic and spontaneous for all reactions based on changes in enthalpy of free energy (ΔG). The binding affinity ( K a ) of debranched waxy maize starch for hexanoic acid decreased with an increase in temperature from 25 to 45°C. The K a and number of binding sites ( n ) for debranched waxy maize exceeded those of potato amylose, indicating a higher complexation of debranched waxy maize for hexanoic acid. The number of binding sites ( n ) and enthalpy of binding (Δ H ) values for both starches remained independent of temperature change. The ITC results demonstrated that debranched waxy maize starch was favored over potato amylose to complex hexanoic acid.

Arijaje, Emily Oluwaseun↗

DOE OSTI2020

Design and Principles of Linear Accelerators and Colliders." in Particle Physics Reference Library, pp. 295-336. Springer, Cham, 2020.

Linear accelerators (linacs) use alternating radiofrequency (RF) electromagnetic fields to accelerate charged particles in a straight line. Linacs were invented about 95 years ago and have seen many significant technical innovations since. A wide range of particle beams have been accelerated with linacs including beams of electrons, positrons, protons, antiprotons, and heavy ions. Linac parameter possibilities include pulsed versus continuous wave, low and high beam powers, low and high repetition rates, low transverse emittance beams, short bunches with small energy spreads, and accelerated multiple bunches in a single pulse. The number of linacs around the world has grown tremendously with thousands of linacs in present use, many for medical therapy, in industry, and for research and development in a broad spectrum of scientific fields. Researchers have developed accelerators for scientific tools in their own right, being awarded several Nobel prizes. Moreover, linacs and particle accelerators in general have enabled many discovery level science experiments in related fields, resulting in many Nobel prizes as well.

Seeman, John↗

DOE OSTI2015

Mass-deformed T N as a linear quiver

The $T_N$ theory is a non-Lagrangian theory with SU(N) flavor symmetry. We argue that when mass terms are given so that two of SU(N)'s are both broken to SU(N-1) x U(1), it becomes $T_{N-1}$ theory coupled to an SU(N-1) vector multiplet together with N fundamentals. This implies that when two of SU(N)'s are both broken to U(1)$^{N-1}$, the theory becomes a linear quiver. We perform various checks of this statement, by using the 5d partition function, the structure of the coupling constants, the Higgs branch, and the Seiberg-Witten curve. We also study the case with more general punctures.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Non Abelian T-duality in Gauged Linear Sigma Models

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. Finally, we analyze the dual models via the geometry of their susy vacua.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Linear sigma dark matter

We present a model of self-interacting dark matter based on QCD-like theories and inspired by the proximity of a 0 (980 ± 20) to the $K\bar{K}$ (990) threshold. Dark matter is comprised of dark pions which self-scatter via the σ resonance close to the ππ threshold. While the linear sigma model serves as a qualitative guide, a fully unitary description of the scattering in the strongly coupled regime is given by effective range theory. The introduction of a kinetically mixed dark photon allows the dark pion to either freeze-out or -in. We study the viable parameter space which explains the observed relic abundance while evading all current constraints. Searches for dark matter self interactions at different scales, (in)direct detection signals, and (in)visibly-decaying dark photons will test this model in the near future.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Stability of linear systems in second-order form based on structure preserving similarity transformations

This paper deals with two stability aspects of linear systems of the form I ¨ x +B˙ x +Cx = 0 given by the triple (I;B;C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I;B1;C1) with a symmetrizable matrix C1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.

Stoustrup, Jakob↗

DOE OSTI2015

Subcellular-level resolution MALDI-MS imaging of maize leaf metabolites by MALDI-linear ion trap-Orbitrap mass spectrometer

A significant limiting factor in achieving high spatial resolution for matrix-assisted laser desorption ionization-mass spectrometry (MALDI-MS) imaging is the size of the laser spot at the sample surface. We present modifications to the beam-delivery optics of a commercial MALDI-linear ion trap-Orbitrap instrument, incorporating an external Nd:YAG laser, beam-shaping optics, and an aspheric focusing lens, to reduce the minimum laser spot size from ~50 μm for the commercial configuration down to ~9 μm for the modified configuration. This improved system was applied for MALDI-MS imaging of cross sections of juvenile maize leaves at 5-μm spatial resolution using an oversampling method. There are a variety of different metabolites including amino acids, glycerolipids, and defense-related compounds were imaged at a spatial resolution well below the size of a single cell. Such images provide unprecedented insights into the metabolism associated with the different tissue types of the maize leaf, which is known to asymmetrically distribute the reactions of C4 photosynthesis among the mesophyll and bundle sheath cell types. The metabolite ion images correlate with the optical images that reveal the structures of the different tissues, and previously known and newly revealed asymmetric metabolic features are observed.

47 OTHER INSTRUMENTATION↗

DOE OSTI2013

Linear Integro-differential Schroedinger and Plate Problems Without Initial Conditions

Via Carleman's estimates we prove uniqueness and continuous dependence results for the temporal traces of solutions to overdetermined linear ill-posed problems related to Schroedinger and plate equation. The overdetermination is prescribed in an open subset of the (space-time) lateral boundary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Kalman Duality Principle for a Class of Ill-Posed Minimax Control Problems with Linear Differential-Algebraic Constraints

In this paper we present Kalman duality principle for a class of linear Differential-Algebraic Equations (DAE) with arbitrary index and time-varying coefficients. We apply it to an ill-posed minimax control problem with DAE constraint and derive a corresponding dual control problem. It turns out that the dual problem is ill-posed as well and so classical optimality conditions are not applicable in the general case. We construct a minimizing sequence <##> } } u }^ } ε $ /hat{u}{sub {/varepsilon}} $ u-hat {sub ε} </##> for the dual problem applying Tikhonov method. Finally we represent <##> } } u }^ } ε $ /hat{u}{sub {/varepsilon}} $ u-hat {sub ε} </##> in the feedback form using Riccati equation on a subspace which corresponds to the differential part of the DAE.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗