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An efficient MILP framework for integrating nonlinear process dynamics and control in optimal production scheduling calculations

The emphasis currently placed on enterprise-wide decision making and optimization has led to an increased need for methods of integrating nonlinear process dynamics and control information in scheduling calculations. The inevitable high dimensionality and nonlinearity of first-principles dynamic process models makes incorporating them in scheduling calculations challenging. In this work, we describe a general framework for deriving data-driven surrogate models of the closed-loop process dynamics. Focusing on Hammerstein–Wiener and finite step response (FSR) model forms, we show that these models can be (exactly) linearized and embedded in production scheduling calculations. The resulting scheduling problems are mixed-integer linear programs with a special structure, which we exploit in a novel and efficient solution strategy. A polymerization reactor case study is utilized to demonstrate the merits of this method. Finally, our framework compares favorably to existing approaches that embed dynamics in scheduling calculations, showing considerable reductions in computational effort.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The Center for Momentum Transport and Flow Organization in Plasmas - Final Scientific Report

Overview of University of Colorado Efforts: The University of Colorado group has focused on two primary fronts during the grant period: development of a variety of multi-point diagnostic and/or imaging analysis techniques, and momentum-transport related experiments on a variety of devices (NSTX at PPPL, CSDX at UCSD, LAPD at UCLA, DIII-D at GA). Experimental work has taken advantage of several diagnostic instruments, including fast-framing cameras for imaging of electron density fluctuations (either directly or using injected gas puffs), ECEI for imaging of electron temperature fluctuations, and multi-tipped Langmuir and magnetic probes for corroborating measurements of Reynolds and Maxwell stresses. Mode Characterization in CSDX: We have performed a series of experiments at the CSDX linear device at UCSD, in collaboration with Center PI G. Tynan's group. The experiments included a detailed study of velocity estimation techniques, including direct comparisons between Langmuir probes and image-based velocimetry from fast-framing camera data. We used the camera data in a second set of studies to identify the spatial and spectral structure of coherent modes, which illuminates wave behavior to a level of detail previously unavailable, and enables direct comparison of dispersion curves to theoretical estimates. In another CSDX study, similar techniques were used to demonstrate a controlled transition from nonlinearly coupled discrete eigenmodes to fully developed broadband turbulence. The axial magnetic field was varied from 40-240 mT, which drove the transition. At low magnetic fields, the plasma is dominated by drift waves. As the magnetic field is increased, a strong potential gradient at the edge introduces an ExB shear-driven instability. At the transition, another mode with signatures of a rotation-induced Rayleigh–Taylor instability appears at the central plasma region. Concurrently, large axial velocities were found in the plasma core. For larger magnetic fields, all of the instabilities co-exist, leading to rich plasma dynamics and fully developed broadband turbulence. Edge-Turbulence and Flow Experiments in NSTX: A series of Gas Puff Imaging (GPI) observations on NSTX revealed a quasi-periodic oscillation in the plasma edge preceding the L-H transition in a limited set of neutral beam heated plasmas. These ~3 kHz flow oscillations exhibit both long wavelength and long correlation lengths, suggesting they are zonal-flow-like. The flow oscillations are strongly correlated with modulations of the level of edge turbulence, thus the system appears to undergo a predator--prey-type limit-cycle preceding the L-H transition. However, a clear trigger for the L-H transition was not observed. Reynolds stress profiles were obtained directly from image velocimetry for L-mode periods ELM-Precursor Studies in NSTX: A separate study based on NSTX-GPI data captured the two-dimensional evolution of edge-localized mode (ELM) precursors. Precursor events were observed preceding ELMs and ELM-induced H–L back-transitions in radio-frequency heated H-mode plasmas, and the growth of the precursor mode through the ELM filamentation was imaged in the plane perpendicular to the local B-field. Strong edge intensity modulations appeared to propagate in the electron diamagnetic direction while steadily drifting radially outwards. Intensity fluctuations were observed at frequencies around 20 kHz and wavenumbers of 0.05-0.2 cm -1 . Upon growing to a trigger point, precursor fluctuations were seen to form filamentary structures and move into the scrape-off layer (SOL) explosively with radial velocities peaking at 8 km/s. Once in the SOL, filaments reverse their propagation direction and travel in the ion diamagnetic direction. Edge intensity fluctuations were strongly correlated with magnetic signals from Mirnov coils, and toroidally distributed coils estimated toroidal mode numbers of n=5-10. Quantitatively similar precursors have been observed in ohmic H-mode plasmas as well, though significantly fewer events are seen in the ohmic cases and none were observed in the near-threshold NBI H-modes studied. Development of Velocimetry and Image Analysis Techniques: Along with the experiments listed above, the Colorado group has continued to explore various velocimetry techniques and their range of validity. We have developed a “linear optical flow” code, which calculates smooth velocity maps while accurately assessing local regions of high curl. This is critical for separating spatial scales of velocity behavior, and thus transport. This code has recently come on-line, and we are currently using it to revisit a number of older datasets. Additionally, we have worked on developing pattern-recognition techniques for imaging diagnostics, based on established digital image compression algorithms. This has the potential to open the analysis of turbulent plasma behavior beyond the well-trodden Fourier and wavelet approaches. Finally, we have extended several of these image-analysis routines to multiple other diagnostic sets, including GPI datasets in NSTX and ECEI imaging on DIII-D. In one study, correlation maps were used to measure the full 2-D mode structure of drift-wave level structures using ECEI for the first time. This enabled direct comparison to gyrokinetic simulations using the GEM code, from which is was determined that TEM modes were being measured in DIII-D.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Domain-decomposition nonlinear manifold reduced order model

This software combines nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD) techniques. NM-ROMs, which utilize a shallow, sparse autoencoder trained with full order model (FOM) snapshot data, approximate the FOM state on a nonlinear manifold. These models offer advantages over linear-subspace ROMs (LS-ROMs) particularly in scenarios with slowly decaying Kolmogorov n-width. However, the training of NM-ROMs involves a number of parameters that scale with the size of the FOM, and storing high-dimensional FOM snapshots can significantly increase the cost of ROM training for extreme-scale problems. To mitigate these costs, the software employs DD to partition the FOM into smaller subdomains, computes NM-ROMs for each, and then integrates these to form a global NM-ROM. This strategy offers multiple benefits: it enables parallel training of subdomain NM-ROMs, reduces the number of parameters needed, decreases the dimensional requirements of subdomain FOM training data, and allows for customization to the unique characteristics of each FOM subdomain. The use of a shallow, sparse autoencoder architecture in each subdomain NM-ROM facilitates the application of hyper-reduction (HR), simplifying the nonlinear complexities and enhancing computational speed. This software marks the inaugural application of NM-ROM combined with HR to a DD problem. It features an algebraic DD reformulation of the FOM, training of NM-ROMs with HR for each subdomain, and employs a sequential quadratic programming (SQP) solver for the evaluation of the coupled global NMROM. The effectiveness of the DD NM-ROM with HR is numerically demonstrated on the 2D steady-state Burgers' equation, showing an order of magnitude improvement in accuracy over the DD LS-ROM with HR.

Diaz, AlejandroN↗

The Physics of Gain Mechanisms in a Self-Amplified Spontaneous Emission Free-Electron Laser

This is the final report for the DoE BES contract DE-FG02-07ER46272. This grant began under a title that gives its history in a few words: The Physics of Gain Mechanisms in a Self-Amplified Spontaneous Emission Free-Electron Laser. At the time of adopting this name, the UCLA Particle Beam Physics Laboratory (PBPL) was at the forefront of the first demonstrations of SASE FEL, giving the experimental basis for the 4th generation X-ray light source now exemplified by the LCLS, a remarkable generation of machines that have revolutionize nanoscale and ultrafast science. The grant title indicates that physical aspects of the FEL are of interest, and implies that progress requires comprehensive investigations. These aspects include: the physics and technology of high brightness electron beam generation, phase space manipulations, advanced beam diagnostics, state-of-the-art undulators, studies of FEL mode characteristics, as well as the introduction of new theoretical models and start-to-end simulations, all yielding a deep understanding of the SASE FEL. The latest period (2010-13) of BES grant support has been the most productive yet for the UCLA PBPL, and the extensive list of accomplishments is illustrative of our central contributions to advanced FEL research. We give a concise overview here and review our research results in further detail below. In FEL and ultrafast beam physics, we have experimentally investigated: production of helical beams and FEL modes with orbital angular momentum; chirp-taper single-spike FEL gain; new FROG techniques optimized for FEL, introduced coherent imaging of beam profiles using transition radiation; and demonstrated a next generation cryoundulator. We have performed deep theoretical studies of these phenomena and other advanced FEL physics concepts, such as the space-charge amplifier. In high brightness beams, we have: introduced a new class of hybrid photoinjector for <100 fs beam production; developed new approaches to self-shaped ellipsoidal beams; used nonlinear plasma oscillations to create beam pulse trains; tested new plasmonic, high quantum efficiency cathodes, and developed new methods of beam measurement with um spatial/sub-fs temporal resolution. In ultrafast imaging, we have: developed advanced electro-optic timing systems, performed the 1st pump-probe study using single shot UED, demonstrated continuously time-resolved UED with RF deflection; made initial use of inverse Compton scattering (ICS) X-ray sources in application through single-shot inline phase contrast imaging, established single-shot X-ray diffraction, and observed ICS high harmonic generation and redshifting due to nonlinear effects. In 5th generation light source research, we have developed the techniques of narrowband, very high power coherent Cerenkov radiation sources based on dielectric wakefield devices. This work is represented by numerous publications in leading journals: e.g. Nature Physics, Physical Review Letters, Applied Physics Letters. The PBPL program’s influence on the field also extends to organization of the electron beam applications community; we have organized the first international UED workshops and the initial two meetings dedicated to 5th generation light source.

43 PARTICLE ACCELERATORS↗

Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film-shape memory alloy composite cantilever plate subjected to in-plane harmonic and stochastic excitation

Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. The goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Ablative Magnetohydrodynamic Rayleigh-Taylor Instability (Final Technical Report)

The Rayleigh-Taylor Instability (RTI) is a ubiquitous flow phenomenon occurring in a multitude of natural and engineered systems in which buoyancy forces exist. RTI is primarily a limiting process in many HED applications and there are significant efforts within the NNSA-ICF program to account for its effect in large scale simulations of ICF implosions both in two- and three-dimensions. The goal of the proposed research is to develop a fundamental understanding of the evolution and role of magnetic fields in the ablative Rayleigh–Taylor instability (aRTI) in the deeply nonlinear stage.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

PETSc/TAO Users Manual V.3.21

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations (PDEs) and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for implementing large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and optimizers that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started ). The library is organized hierarchically, enabling users to employ the abstraction level most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users.

97 MATHEMATICS AND COMPUTING↗

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗

First principles crystal engineering of nonlinear optical materials. I. Prototypical case of urea

The crystalline materials with nonlinear optical (NLO) properties are critically important for several technological applications, including nanophotonic and second harmonic generation devices. Urea is often considered to be a standard NLO material, due to the combination of non-centrosymmetric crystal packing and capacity for intramolecular charge transfer. Various approaches to crystal engineering of non-centrosymmetric molecular materials were reported in the literature. Here we propose using global lattice energy minimization to predict the crystal packing from the first principles. We developed a methodology that includes the following: (1) parameter derivation for polarizable force field AMOEBA; (2) local minimizations of crystal structures with these parameters, combined with the evolutionary algorithm for a global minimum search, implemented in program USPEX; (3) filtering out duplicate polymorphs produced; (4) reoptimization and final ranking based on density functional theory (DFT) with many-body dispersion (MBD) correction; and (5) prediction of the second-order susceptibility tensor by finite field approach. This methodology was applied to predict virtual urea polymorphs. After filtering based on packing similarity, only two distinct packing modes were predicted: one experimental and one hypothetical. DFT + MBD ranking established non-centrosymmetric crystal packing as the global minimum, in agreement with the experiment. Finite field approach was used to predict nonlinear susceptibility, and H-bonding was found to account for a 2.5-fold increase in molecular hyperpolarizability to the bulk value.

36 MATERIALS SCIENCE↗

The time-resolved atomic, molecular and optical science instrument at the Linac Coherent Light Source

The newly constructed time-resolved atomic, molecular and optical science instrument (TMO) is configured to take full advantage of both linear accelerators at SLAC National Accelerator Laboratory, the copper accelerator operating at a repetition rate of 120 Hz providing high per-pulse energy as well as the superconducting accelerator operating at a repetition rate of about 1 MHz providing high average intensity. Both accelerators power a soft X-ray free-electron laser with the new variable-gap undulator section. With this flexible light source, TMO supports many experimental techniques not previously available at LCLS and will have two X-ray beam focus spots in line. Thereby, TMO supports atomic, molecular and optical, strong-field and nonlinear science and will also host a designated new dynamic reaction microscope with a sub-micrometer X-ray focus spot. The flexible instrument design is optimized for studying ultrafast electronic and molecular phenomena and can take full advantage of the sub-femtosecond soft X-ray pulse generation program.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SISGR: Atom chip microscopy: A novel probe for strongly correlated materials

Microscopy techniques co-opted from nonlinear optics and high energy physics have complemented solid-state probes in elucidating the order manifest in condensed matter materials. Up until now, however, no attempts have been made to use modern techniques of ultracold atomic physics to directly explore properties of strongly correlated or topologically protected materials. Our current program is focused on introducing a novel magnetic field microscopy technique into the toolbox of imaging probes. Our prior DOE ESPM program funded the development of a novel instrument using a dilute gas Bose-Einstein condensate (BEC) as a scanning probe capable of measuring tiny magnetic (and electric) DC and AC fields above materials. We successfully built the world's first “scanning cryogenic atom chip microscope”, and we now are in the process of characterizing its performance before using the instrument to take the first wide-area images of transport flow within unconventional superconductors, pnictides and oxide interfaces (LAO/STO), topological insulators, and colossal magnetoresistive manganites. We will do so at temperatures outside the capability of scanning SQUIDs, with ~10x better resolution and without 1/f-noise. A notable goal will be to measure the surface-to-bulk conductivity ratio in topological insulators in a relatively model-independent fashion. We have completed the construction of this magnetic microscope. The instrument uses atom chips—substrates supporting micron-sized current-carrying wires that create magnetic microtraps near surfaces for ultracold thermal gases and BECs—to enable single-shot and raster-scanned large-field-of-view detection of magnetic fields. The fields emanating from electronic transport may be detected at the 10 -7 flux quantum (Φ0) level and below; that is, few to sub-micron resolution of sub-nanotesla fields over single-shot, millimeter-long detection lengths. By harnessing the extreme sensitivity of atomic clocks and BECs to external perturbations, we are now in a position to use atom chips for imaging transport in new regimes. Scanning quantum gas atom chip microscopy introduces three very important features to the toolbox of high-resolution scanning microscopy of strongly correlated or topological materials: simultaneous detection of magnetic and electric fields (down to the sub-single electron charge level; no invasive large magnetic fields or gradients; simultaneous micro- and macroscopic spatial resolution; DC to MHz detection bandwidth; freedom from 1/ƒ flicker noise at low frequencies; and, perhaps most importantly, the complete decoupling of probe and sample temperatures. The atom chip microscope can operate at maximum sensitivity and resolution without regard to the substrate temperature. While the BEC is among the coldest objects realizable (100 nK temperatures are typical), the atom chip substrate can be positioned 1 μm away from the BEC and be as hot as 400 K or as cold as the cryostat can cool. This is because unlike superconducting probes, whose temperature is closely coupled to nearby materials, quantum gases are immune to radiative heating. The energy gap between a Rb atom’s ground state and first excited state far exceeds the typical energy of room-temperature blackbody radiation; such atoms are therefore transparent to radiation heating by materials at room temperature or below. We experimentally demonstrated a new atom chip trapping system that allows the placement and high-resolution imaging of ultracold atoms within microns from any ≤100 μm-thin, UHV-compatible material, while also allowing sample exchange with minimal experimental downtime. The sample is not connected to the atom chip, allowing rapid exchange without perturbing the atom chip or laser cooling apparatus. Exchange of the sample and retrapping of atoms has been performed within a week turnaround, limited only by chamber baking. Moreover, the decoupling of sample and atom chip provides the ability to independently tune the sample temperature and its position with respect to the trapped ultracold gas, which itself may remain in the focus of a high-resolution imaging system. We confine 100-nK BECs of 104 87Rb atoms near a gold-mirrored 100-μm-thick silicon substrate. The substrate can be cooled to 35 K without use of a heat shield, while the atom chip, 120-μm away, remains at room temperature. Atoms may be imaged with 1-μm resolution and retrapped every 16 s, allowing rapid data collection. Straightforward improvements will allow us to push sample temperatures close to 4 K, and improve imaging resolution from 1 μm down to a few-100 nm, thereby providing 10 -9 Φ0 detection sensitivity. We will test the utility of this technique by imaging the magnetic fields emanating from electronic transport and domain percolation in several interesting examples of strongly correlated or topologically protected materials. STM, transport, and x-ray scattering experiments have, among others, revealed the existence of a quantum liquid crystal state in iron (pnictide) and cuprate superconductors. This strongly correlated state of matter could also be detected by imaging the fluctuating transport (spatially and in time) of electrons as the phase/regime boundary is crossed between the pnictide non-Fermi liquid (cuprate strange metal) and the pnictide magnetic phase (cuprate pseudogap regime). Our ability to image wide-area inhomogeneous current flow from room-temperature to <10 K will allow us to study the developing domain structure and transport near twin boundary interfaces through the T N ≈50–150 K nematic transition recently identified in bulk transport experiments by Ian Fisher's group in underdoped Fe-arsinide superconductors. Again, this highlights a main feature of our cryogenic atom chip microscope: the ability to image transport regardless of the sample temperature since the BEC, at nK temperatures, is transparent to blackbody radiation, even when held a microns from the surface.

36 MATERIALS SCIENCE↗

The Integrable Optics Test Accelerator

The Integrable Optics Test Accelerator (IOTA) at the Fermilab Accelerator Science & Technology (FAST) Facility is beginning operations, with an experimental program aimed at developing technology to enable future high intensity particle beams. The results garnered from IOTA should allow for better control of beam losses, leading to higher safely achievable beam power. This will be particularly useful for future accelerator based neutrino experiments. Two of the R&D efforts at IOTA, Nonlinear Integrable Optics and Electron Column-based space charge compensation, are discussed here.

43 PARTICLE ACCELERATORS↗

2012 Gordon Research Conference on Vibrational Spectroscopy - Formal Schedule and Speaker/Poster Program

The Vibrational Spectroscopy conference brings together experimentalists and theoreticians working at the frontiers of modern vibrational spectroscopy, with a special emphasis on spectroscopies that probe the structure and dynamics of molecules in gases, liquids, and at interfaces. The conference explores the wide range of state-of-the-art techniques based on vibrational motion. These techniques span the fields of time-domain, high-resolution frequency-domain, spatially-resolved, nonlinear, and multidimensional spectroscopies. The conference highlights both the application of these techniques in chemistry, materials, biology, the environment, and medicine as well as the development of theoretical models that enable one to connect spectroscopic signatures to underlying molecular motions including chemical reaction dynamics. The conference goal is to advance the field of vibrational spectroscopy by bringing together a collection of researchers who share common interests and who will gain from discussing work at the forefront of several connected areas. The intent is to emphasize the insights and understanding that studies of vibrations provide about a variety of molecular systems ranging from small polyatomic molecules to large biomolecules, nanomaterials, and environmental systems.

74 ATOMIC AND MOLECULAR PHYSICS↗

Optimal Power Flow of Radial Networks and Its Variations: A Sequential Convex Optimization Approach

This paper proposes a sequential convex optimization method to solve broader classes of optimal power flow (OPF) problems over radial networks. The non-convex branch power flow equation is decomposed as a second-order cone inequality and a non-convex constraint involving the difference of two convex functions. Provided with an initial solution offered by an inexact second-order cone programming relaxation model, this approach solves a sequence of convexified penalization problems, where concave terms are approximated by linear functions and updated in each iteration. It could recover a feasible power flow solution, which usually appears to be very close, if not equal, to the global optimal one. Two variations of the OPF problem, in which non-cost related objectives are optimized subject to power flow constraints and the convex relaxation is generally inexact, are elaborated in detail. One is the maximum loadability problem, which is formulated as a special OPF problem that seeks the maximal distance to the boundary of power flow insolvability. The proposed method is shown to outperform commercial nonlinear solvers in terms of robustness and efficiency. The other is the bi-objective OPF problem. A non-parametric scalarization model is suggested, and is further reformulated as an extended OPF problem by convexifying the objective function. It provides a single trade-off solution without any subjective preference. The proposed computation framework also helps retrieve the Pareto front of the bi-objective OPF via the e-constraint method or the normal boundary intersection method. This paper also discusses extensions for OPF problems over meshed networks based on the semidefinite programming relaxation method.

bi-objective optimization↗

Testing nuclear parton distributions with pA collisions at the TeV scale

Global perturbative QCD analyses, based on large data sets from electron-proton and hadron collider experiments, provide tight constraints on the parton distribution function (PDF) in the proton. The extension of these analyses to nuclear parton distribution functions (nPDFs) has attracted much interest in recent years. nPDFs are needed as benchmarks for the characterization of hot QCD matter in nucleus-nucleus collisions, and attract further interest since they may show novel signatures of nonlinear density-dependent QCD evolution. However, it is not known from first principles whether the factorization of long-range phenomena into process-independent parton distribution, which underlies global PDF extractions for the proton, extends to nuclear effects. As a consequence, assessing the reliability of nPDFs for benchmark calculations goes beyond testing the numerical accuracy of their extraction and requires phenomenological tests of the factorization assumption. Here, we argue that a proton-nucleus collision program at the Large Hadron Collider would provide a set of measurements, which allow for unprecedented tests of the factorization assumption, underlying global nPDF fits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reduced Dimensionality Lithium Niobate Microsystems

The following report describes work performed under the LDRD program at Sandia National Laboratories October 2014 and September 2016. The work presented demonstrates the ability of Sandia Labs to develop state-of-the-art photonic devices based on thin film lithium niobate (LiNbO 3 ). Section 1 provides an introduction to integrated LiNbO 3 devices and motivation for developing thin film nonlinear optical systems. Section 2 describes the design, fabrication, and photonic performance of thin film optical microdisks fabricated from bulk LiNbO 3 using a bulk implantation method developed at Sandia. Sections 3 and 4 describe the development of similar thin film LiNbO 3 structures fabricated from LiNbO 3 on insulator (LNOI) substrates and our demonstration of optical frequency conversion with state-of-the-art efficiency. Finally, Section 5 describes similar microdisk resonators fabricated from LNOI wafers with a buried metal layer, in which we demonstrate electro-optic modulation.

36 MATERIALS SCIENCE↗