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Recent advances in computational mathematics and applications

We are honored to bring you this special issue dedicated to recent advances in computational mathematics and applications in science and engineering. The papers in this special issue were presented in ”Conference on Computational Mathematics and Applications (CCMA)” held at the University of Nevada Las Vegas (UNLV) during October 25–27, 2019. The conference has attracted about 90 attendees from six countries. The 15 papers in the special issue comprise a diverse collection of theoretical numerical analysis as well as applications in various subjects. Topics cover optimal control of PDEs, discontinuous Galerkin methods, fluid flow in porous media, turbulence flow, static and moving interface problems, complex fluids composed by the mixture of Newtonian fluid and nematic (liquid crystal) flows, modeling of ocean–atmosphere system, image segmentation algorithm, uncertainty quantification problems for turbulence model and Maxwell’s equations, iterative solver for systems resulting from mixed methods, and novel methods for solving systems of nonlinear equations. As the Guest Editors we would like to thank Dr. Leland Jameson at NSF (National Science Foundation) for kindly supporting our conference proposal which made this conference possible. We would also like to thank Darren Sugrue from Elsevier who provided partial support for our conference, and Thennarasu Gunasekaran and his production team from Elsevier who produced this nice special issue. We are grateful to many people (Dr. Zhijian Wu, Lori Ornelas, Elsa Juarez, and many Ph.D. students) at the Department of Mathematical Sciences of UNLV who provided tremendous support for the conference. Finally, we very much appreciate all authors who contributed their precious results to this special issue.

97 MATHEMATICS AND COMPUTING↗

GaAs Thermophotovoltaic Patterned Dielectric Back Contact Devices with Improved Sub-Bandgap Reflectance

We demonstrate GaAs thermophotovoltaic (TPV) devices with a patterned dielectric back contact (PDBC) architecture, featuring a dielectric spacer between the semiconductor and back metal contact over most of the back surface for high reflectance, and metal point contacts over a smaller area for electrical conduction. In the TPV application, high sub-bandgap reflectance is needed to reflect unused sub-bandgap photons to the thermal emitter to minimize energy losses in this portion of the thermal spectrum. We explore different PDBC fabrication processes with SU-8 and SiO2 dielectric spacer layers to maximize sub-bandgap reflectance while minimizing series resistance to increase TPV conversion efficiency. We successfully demonstrate GaAs SU-8 PDBC TPV devices with 2200 degrees C blackbody-weighted sub-bandgap reflectance of 94.9% and 96.5% with and without a front metal grid, respectively. This is 0.7% and 2.3% (absolute) higher than the mean sub-bandgap reflectance of 94.2% for GaAs baseline TPV devices with 100% Au back contact with front metal grid. Lower sub-bandgap reflectance in TPV devices with front grids indicates the front grid induces light scattering leading to additional parasitic absorption in the TPV device. We also show that for higher contact coverage fractions, the PDBC reflectance cannot in general be treated by a linear interpolation using simple 1D transfer matrix method modeling and should be treated instead as a diffraction grating by solving Maxwell's equations in 3D.

energy storage↗

Plasma-based prism compressor design for high-intensity laser pulses

A concept for a femtosecond pulse compressor based on underdense plasma prisms is presented. An analytical model is developed to calculate the spectral phase incurred and the expected pulse compression. A 2D particle-in-cell simulation verifies the analytical model. Simulated intensities ( ∼10 16 W/cm 2 ) were orders of magnitude higher than the damage threshold for conventional gratings used in chirped pulse amplification. Theoretical geometries for compact (tens of cm scale) compressors for 1, 10 and 100 PW power levels are proposed.

47 OTHER INSTRUMENTATION↗

Scattering of radiofrequency waves by randomly modulated density interfaces in the edge of fusion plasmas

In the scrape-off layer and the edge region of a tokamak, the plasma is strongly turbulent and scatters the radiofrequency (RF) electromagnetic waves that propagate through this region. It is important to know the spectral properties of these scattered RF waves, whether used for diagnostics or for heating and current drive. The spectral changes influence the interpretation of the obtained diagnostic data, and the current and heating profiles. A full-wave, three-dimensional (3-D) electromagnetic code ScaRF has been developed for studying the RF wave propagation through turbulent plasma. ScaRF is a finite-difference frequency-domain (FDFD) method used for solving Maxwell's equations. The magnetized plasma is defined through the cold plasma by the anisotropic permittivity tensor. As a result, ScaRF can be used to study the scattering of any cold plasma RF wave. It can also be used for the study of the scattering of electron cyclotron waves in ITER-type and medium-sized tokamaks such as TCV, ASDEX-U and DIII-D. For the case of medium-sized tokamaks, there is experimental evidence that drift waves and rippling modes are present in the edge region. Hence, we have studied the scattering of RF waves by periodic density interfaces (plasma gratings) in the form of a superposition of spatial modes with varying periodicity and random amplitudes. The power reflection coefficient (a random variable) is calculated for different realizations of the density interface. In this work, the uncertainty of the power reflection coefficient is rigorously quantified by use of the Polynomial Chaos Expansion method in conjunction with the Smolyak sparse-grid integration, which is known as the PCE-SG method. The PCE-SG method is proven to be accurate and more efficient compared with alternative methods such as the Monte Carlo (MC) approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Detecting Thermally Induced Spinodal Decomposition with Picosecond Ultrasonics in Cast Austenitic Stainless Steels

Given the existential climate crisis faced by mankind and the world, the lifetime and sustainability of nuclear reactors as a carbon-free source of renewable energy depend on the susceptibility of their structural components to environmental degradation. In particular, critical components for light water reactors (LWRs) evolve over decades in service, losing ductility and toughness due to thermal and irradiation aging. Techniques to monitor their health cannot be easily applied in the field due to their destructive, expensive, or immobile nature. Thus, non-destructive evaluation (NDE) methods are sought to monitor and evaluate the health of major LWR components such as core barrels, steam generator tubes, or primary coolant pipes and are often required by policy, such as NRC policy #10-CFR-50.65. In this work we demonstrate the use of gigahertz, non-contact ultrasonics to gauge the state of cast austenitic stainless steels (CASS), used in some of the largest components in LWR primary systems. We do so by linking changes in their surface acoustic wave (SAW) characteristics using transient grating spectroscopy (TGS) to transmission electron microscopy (TEM)-verified evidence of spinodal decomposition and G-phase precipitation. In this thesis, thermal aging is shown to induce SAW peak splitting in spinodally decomposed CASS alloys, correlated strongly with lowered toughness and decreased ductility. Furthermore, statistical testing on the number of SAW peak splits observed show that the second SAW peak significantly appears more frequently and is significantly different in frequency in comparison to counts and frequencies measured in unaged specimens. The ability of this technique to non-destructively detect microstructural degradation at a distance in a predictive manner in the case of CASS motivates extending gigahertz ultrasonics to detect other LWR material degradation modes as an in-vessel inspection technique, such as reactor pressure vessel (RPV) embrittlement. This allows for the greater use of NDE techniques for confident monitoring of LWR structural material health to 80 years and beyond, saving costs by minimizing structural replacements until needed and maximizing energy production by preventing early decommission until necessary.

36 MATERIALS SCIENCE↗

Correction to Reconciling Work Functions and Adsorption Enthalpies for Implicit Solvent Models: A Pt (111)/Water Interface Case Study

This errata is to correct the acknowledgment in the original published article. G.B. (partial support), V.-A.G., M.-T.N., and R.R. were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division. Computer resources were provided by Research Computing at Pacific Northwest National Laboratory and the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. PNNL is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830. G.B. acknowledges the EPSRC for partial support in PhD funding. The authors acknowledge the use of the IRIDIS High Performance Computing Facility (IRIDIS 5) and associated support services at the University of Southampton in the completion of this work. We are grateful to the UK Materials and Molecular Modeling Hub (Thomas HPC) for computational resources, which is partially funded by EPSRC (EP/P020194/1).

continuum solvation, metal/water interfaces, ab in↗

Electroluminescence and Plasmon-Assisted Directional Photoluminescence from 2D HgTe Nanoplatelets

In the visible range, 2D nanoplatelets (NPLs) have brought significant benefits compared to their 0D counterpart with an inherently anisotropic emission, a narrower photoluminescence (PL) signal, and new degrees of freedom to design heterostructures. Compared to the properties of cadmium chalcogenide NPLs in the visible, similar research is still mostly lacking in the infrared, in spite of existing synthetic paths to obtain narrow band gap semiconductors in 2D colloidal form. Here, in this paper, we focus on 2D HgTe NPLs and show how their PL can be stabilized through the proper choice of surface chemistry. We then demonstrate two important steps toward bright infrared light emitting diodes (LEDs) which are (i) the coupling to a plasmonic grating to control the magnitude and spatial direction of the PL signal and (ii) the observation of electroluminescence at 1300 nm, which is near telecom wavelength.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Inverse-Designed Nanophotonic Interface for Excitons in Atomically Thin Materials

Efficient nanophotonic devices are essential for applications in quantum networking, optical information processing, sensing, and nonlinear optics. Extensive research efforts have focused on integrating two-dimensional (2D) materials into photonic structures, but this integration is often limited by size and material quality. Here, we use hexagonal boron nitride (hBN), a benchmark choice for encapsulating atomically thin materials, as a waveguiding layer while simultaneously improving the optical quality of the embedded films. When combined with a photonic inverse design, it becomes a complete nanophotonic platform to interface with optically active 2D materials. Grating couplers and low-loss waveguides provide optical interfacing and routing, tunable cavities provide a large exciton-photon coupling to transition metal dichalcogenide (TMD) monolayers through Purcell enhancement, and metasurfaces enable the efficient detection of TMD dark excitons. This work paves the way for advanced 2D-material nanophotonic structures for classical and quantum nonlinear optics.

2D materials↗

Self-Trapped-Exciton Radiative Recombination in β–Ga 2 O 3 : Impact of Two Concurrent Nonradiative Auger Processes

The peculiarities of radiative and nonradiative processes associated with self-trapped intrinsic eXcitons in the excited β-Ga 2 O 3 crystals are studied via time-resolved techniques of induced absorption, transient grating, and photoluminescence (PL) at room temperature. The excitation above the bandgap is produced by laser pulses with linear light polarization parallel and orthogonal in the (–201) and (001) planes. We elucidate that the nonradiative recombination rate occurring in the eXciton prevails over its radiative emission rate in a wide range of free carrier concentration composed of excited and equilibrium electrons. Hence, the nonradiative recombination has no effect on the strong anisotropy and the shape of the eXciton emission band. However, we find out that the conventional ABC model of electron effective lifetime is insufficient for explanation of the excitation dependences. Inclusion of two nonradiative Auger mechanisms in a modified ABC formula provides excellent agreement of these dependences. We conclude that the trap-assisted Auger process is in proportion to the free electron density with coefficient B = 1.1 × 10 –11 cm 3 /s and appears at low/intermediate excitation, while the triple-particle Auger process is in proportion to Δn 2 with coefficient C = 8 × 10 –30 cm 6 /s and appears at high excitation conditions. The transition between two Auger mechanisms is accompanied by a rise of the eXciton diffusivity in preferred crystallographic directions where the radiative PL intensity is maximal. The diffusion length LD in these directions can reach values ~300 nm, but, at high excitations, LD becomes limited by Auger lifetimes. These findings pave the way for the implementation of self-trapped eXcitons into specific optoelectronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of Networking Density on the Patterning Performance of Molecular Layer Deposited Alucone Electron Beam/EUV Resists

One of the main barriers to continued device scaling in the era of extreme ultraviolet (EUV) lithography is the need for improved photoresist chemistries to address challenges such as poor EUV sensitivity, inadequate etch resistance, and pattern collapse. Metal-organic photoresists are a promising class of materials that can address many of these challenges, and among them, resists deposited via hybrid molecular layer deposition (MLD) have attracted interest for their unique advantages in thickness control, chemical homogeneity, and compatibility with vacuum processing. However, despite many successful demonstrations of patterning, little is known about how the molecular design of hybrid MLD resists affects their lithographic performance. In this work, we study the effect of the network structure, a common feature among all hybrid MLD resists, via a series of aluminum alkoxide ("alucone") negative tone resists with varying networking density. Their patterning mechanism is investigated via electron beam lithography (EBL)─a common proxy for EUV─and compared to their EUV-induced reactions studied via flood exposure and in situ characterization. In conclusion, we show that the resist with the least networking density demonstrates the best sensitivity and resolution, with the ability to resolve dense line/space gratings as small as 14 nm half pitch via EBL.

electron beam lithography↗

High Resolution Infrared Spectroscopy of Highly Reactive Chemical Intermediates: Berkeley Inspiration and a C.B. Moore Retrospective

One of the long-standing paradoxes in chemistry is that the molecular species of greatest interest are often highly reactive chemical intermediates and thus present only at vanishingly small concentrations under typical steady state conditions. Here, this has proven both a key frustration and powerful motivation for physical chemists in probing such species, particularly for high resolution laser spectroscopic methods in the infrared. Over the past 4-5 decades, this fundamental sensitivity challenge has stimulated the development of many novel techniques for efficient generation, cooling, and infrared probing of such transient chemical intermediates, achieving increasingly sophisticated levels of spectroscopic detail, chemical insight, and a testbed for comparison with first principles ab initio quantum calculations. Two of the pioneering contributors to this scientific arena have been George Pimentel and C. Bradley Moore, both responsible for nourishing DJN’s own enduring fascination with spectroscopic IR study of elusive chemical intermediates. This chapter is not intended to provide a comprehensive review of this large and enormously successful field, but it rather more simply attempts to capture a few selective “Moore-centric” snapshots of the Nesbitt group scientific evolution, specifically in i) advances by Pimentel for the original development of rapid scan flash kinetic spectroscopy based on spectrometers with rapidly rotating IR gratings, ii) the modernization/extension of these methods in the Moore group toward the first high resolution IR laser spectroscopy of singlet/triplet methylene 1,3 CH 2 diradical, and finally to iii) the development of slit supersonic discharge expansion methods at JILA for sub-Doppler infrared laser study of multiple radicals, jet cooled molecular ions, and highly reactive chemical intermediates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Direct Optical Lithography of Colloidal Metal Oxide Nanomaterials for Diffractive Optical Elements with 2π Phase Control

Spatially patterned dielectric materials are ubiquitous in electronic, photonic, and optoelectronic devices. These patterns are typically made by subtractive or additive approaches utilizing vapor-phase reagents. On the other hand, recent advances in solution-phase synthesis of oxide nanomaterials have unlocked a materials library with greater compositional, microstructural, and interfacial tunability. However, methods to pattern and integrate these nanomaterials in real-world devices are less established. In this work, we directly optically pattern oxide nanoparticles (NPs) by mixing them with photosensitive diazo-2-naphthol-4-sulfonic acid and irradiating with widely available 405 nm light. We demonstrate the direct optical lithography of ZrO 2 , TiO 2 , HfO 2 , and ITO NPs and investigate the chemical and physical changes responsible for this photoinduced decrease in solubility. Micron-thick layers of amorphous ZrO 2 NPs were patterned with micron resolution and shown to allow 2 pi phase control of visible light. We also show multilayer patterning and use it to fabricate features with different thicknesses and distinct structural colors. Upon annealing at 400 degrees C, the deposited ZrO 2 structures have excellent optical transparency across a wide wavelength range (0.3-10 mu m), a high refractive index (n = 1.84 at 633 nm), and are optically smooth. We then fabricate diffractive optical elements, such as binary phase diffraction gratings, that show efficient diffractive behavior and good thermal stability. Different oxide NPs can also be mixed prior to patterning, providing a high level of material tunability. This work demonstrates a general patterning approach that harnesses the processability and diversity of colloidal oxide nanomaterials for use in photonic applications.

2𝜋 phase shift↗

Stimulus edges induce orientation tuning in superior colliculus

Orientation columns exist in the primary visual cortex (V1) of cat and primates but not mouse. Intriguingly, some recent studies reported the presence of orientation and direction columns in the mouse superficial superior colliculus (sSC), while others reported a lack of columnar organization therein. Using in vivo calcium imaging of sSC in the awake mouse brain, we found that the presence of columns is highly stimulus dependent. Specifically, we observed orientation and direction columns formed by sSC neurons retinotopically mapped to the edge of grating stimuli. For both excitatory and inhibitory neurons in sSC, orientation selectivity can be induced by the edge with their preferred orientation perpendicular to the edge orientation. Furthermore, we found that this edge-induced orientation selectivity is associated with saliency encoding. These findings indicate that the tuning properties of sSC neurons are not fixed by circuit architecture but rather dependent on the spatiotemporal properties of the stimulus.

59 BASIC BIOLOGICAL SCIENCES↗

Time-of-flight detection of terahertz phonon-polariton

A polariton is a fundamental quasiparticle that arises from strong light-matter interaction and as such has attracted wide scientific and practical interest. When light is strongly coupled to the crystal lattice, it gives rise to phonon-polaritons (PPs), which have been proven useful in the dynamical manipulation of quantum materials and the advancement of terahertz technologies. Yet, current detection and characterization methods of polaritons are still limited. Traditional techniques such as Raman or transient grating either rely on fine-tuning of external parameters or complex phase extraction techniques. To overcome these inherent limitations, we propose and demonstrate a technique based on a time-of-flight measurement of PPs. We resonantly launch broadband PPs with intense terahertz fields and measure the time-of-flight of each spectral component with time-resolved second harmonic generation. The time-of-flight information, combined with the PP attenuation, enables us to resolve the real and imaginary parts of the PP dispersion relation. We demonstrate this technique in the van der Waals magnets NiI 2 and MnPS 3 and reveal a hidden magnon-phonon interaction. We believe that this approach will unlock new opportunities for studying polaritons across diverse material systems and enhance our understanding of strong light-matter interaction.

condensed-matter physics↗

Single-shot magnon interference in a magnon-superconducting-resonator hybrid circuit

Magnon interference is a hallmark of coherent magnon interactions. In this work, we demonstrate single-shot magnon interference using up to four magnon pulses in two remotely coupled yttrium iron garnet spheres mediated by a coplanar superconducting resonator. By exciting one YIG sphere with injected microwave pulses, we achieve coherent energy exchange between the two spheres, facilitating their interference processes, including Rabi-like oscillation with a single pulse, constructive and destructive interference with two pulses, and interference peak sharpening with up to four pulses—analogous to diffraction grating in optical interference. The resulting interference patterns can be precisely controlled by changing the frequency detuning and time delay of the magnon pulses. The demonstration of time-domain coherent control of remote magnon interference opens new pathways for advancing coherent information processing through multi-operation, circuit-integrated hybrid magnonic networks.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Geometric control of hyperbolic exciton-polariton condensate dimers

Coupled many-body quantum systems exhibit rich emergent physics with diverse stationary and dynamical behaviours. By engineering platforms with tunable and distinct coupling mechanisms, new insights emerge into the collective behaviour of coupled many body systems. Particles can be exchanged via evanescent or ballistic coupling: the former, based on proximity, yields large spectral splitting, while the latter requires strict phase-matching, analogous to phase-coupled harmonic oscillators and has a smaller impact on the energy landscape. We demonstrate an all-optically tunable quantum fluid dimer based on exciton-polariton condensates in a photonic crystal waveguide with hyperbolic (saddle-like) dispersion. Varying the dimer’s angle relative to the grating tunes the coupling from evanescent to ballistic. We directly observe spectral features and mass flow shaped by the saddle dispersion. This work highlights photonic crystals as powerful platforms to explore condensed matter phenomena lying at the interface between delay-coupled nonlinear oscillators and tight binding physics.

Georgakilas, Ioannis [IBM Research-Zurich, Rüschli↗

Beating absorption in solid-state high harmonics

Since the new millennium coherent extreme ultra-violet and soft x-ray radiation has revolutionized the understanding of dynamical physical, chemical and biological systems at the electron’s natural timescale. Unfortunately, coherent laser-based upconversion of infrared photons to vacuum-ultraviolet and soft x-ray high-order harmonics in gaseous, liquid and solid targets is notoriously inefficient. In dense nonlinear media, the limiting factor is strong re-absorption of the generated high-energy photons. Here we overcome this limitation by generating high-order harmonics from a periodic array of thin one-dimensional crystalline silicon ridge waveguides. Adding vacuum gaps between the ridges avoids the high absorption loss of the bulk and results in a ~ 100-fold increase of the extraction depth. As the grating period is varied, each high harmonic shows a different and marked modulation, indicating their waveguiding in the vacuum slots with reduced absorption. Looking ahead, our results enable bright on-chip coherent short-wavelength sources and may extend the usable spectral range of traditional nonlinear crystals to their absorption windows. Potential applications include on-chip chemically-sensitive spectro-nanoscopy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Mirrors for petawatt lasers: Design principles, limitations, and solutions

High intensity and high energy laser facilities place increasing demands on optical components, requiring large surface area optics with exacting specifications. Petawatt lasers are high energy, short-pulse laser systems generally based on chirped-pulse amplification, where an initial low energy short pulse is stretched, amplified, and then recompressed to produce fs to ps high-power laser pulses. In such petawatt lasers, the highest demands are placed on the final optics, including gratings which compress the pulses and mirrors which direct and focus the final high-power beams. The limiting factor in these optical components is generally laser-induced damage. Designing and fabricating these optical components to meet reflection, dispersion, and other requirements while meeting laser-induced damage requirements is the primary challenge discussed in this tutorial. We will introduce the reader to the technical challenges and tradeoffs required to produce mirrors for petawatt lasers and discuss current research directions.

47 OTHER INSTRUMENTATION↗